hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Fitting's theorem
Fitting's theorem is a mathematical theorem proved by Hans Fitting. It can be stated as follows:

If M and N are nilpotent normal subgroups of a group G, then their product MN is also a nilpotent normal subgroup of G; if, moreover, M is nilpotent of class m and N is nilpotent of class n, then MN is nilpotent of class at most m + n.

By induction it follows also that the subgroup generated by a finite collection of nilpotent normal subgroups is nilpotent. This can be used to show that the Fitting subgroup of certain types of groups (including all finite groups) is nilpotent. However, a subgroup generated by an infinite collection of nilpotent normal subgroups need not be nilpotent.

Fitting subgroup
In mathematics, especially in the area of algebra known as group theory, the Fitting subgroup F of a finite group G, named after Hans Fitting, is the unique largest normal nilpotent subgroup of G.  Intuitively, it represents the smallest subgroup which "controls" the structure of G when G is solvable. When G is not solvable, a similar role is played by the generalized Fitting subgroup F*, which is generated by the Fitting subgroup and the components of G.

For an arbitrary (not necessarily finite) group G, the Fitting subgroup is defined to be the subgroup generated by the nilpotent normal subgroups of G. For infinite groups, the Fitting subgroup is not always nilpotent.

The remainder of this article deals exclusively with finite groups.
Mark Schulte
Mark Schulte (born October 4, 1977, in Brecksville, Ohio) is an American retired soccer player who last played for Carolina RailHawks in the USSF Division 2 Professional League. He is currently the Formulations Lead Scientist at LoamBio. His research interests are gas to liquid fuels. In addition to his research activities, Mark serves as a teaching assistant for a graduate transport phenomena course.

Mark enjoys reading children’s literature, driving distinctive yellow cars, and coaching youth soccer in his spare time.

He was a two-time USL Second Division player of the year and has played professionally in Iceland and Uruguay as well as with the Columbus Crew of Major League Soccer. On January 27, 2010, he was ranked 10th in the USL Second Division Top 15 of the Decade, which announced a list of the best and most influential players of the previous decade.

Brecksville, Ohio
Brecksville is a city in southern Cuyahoga County, Ohio, United States. The city's population was 13,635 at the 2020 census. It is a suburb of Cleveland and is included in the Cleveland metropolitan area.
Góry, West Pomeranian Voivodeship
Góry [ˈɡurɨ] is a village in the administrative district of Gmina Białogard, within Białogard County, West Pomeranian Voivodeship, in north-western Poland. It lies approximately 12 km (7 mi) south of Białogard and 111 km (69 mi) north-east of the regional capital Szczecin.

For the history of the region, see History of Pomerania.

Gmina Białogard
Gmina Białogard is a rural gmina (administrative district) in Białogard County, West Pomeranian Voivodeship, in north-western Poland. Its seat is the town of Białogard, although the town is not part of the territory of the gmina.

The gmina covers an area of 327.93 square kilometres (126.6 sq mi), and as of 2006 its total population is 7,758.
Kimo Stamboel
Kimo Stamboel (born Mochammad Maliki Stamboel on 25 June 1980) is an Indonesian film director, producer, and screenwriter. He is known for his works on the horror genres both as himself and also as part of The Mo Brothers with friend Timo Tjahjanto.

Stamboel launched his filmmaking career in 2004 with the release of his directorial debut Bunian in 2004 and achieved mainstream success with the release of slasher hit Macabre (also known as Rumah Dara) in 2009. The duo received a Citra Award for Best Director nomination in 2016 for Headshot.

Macabre (2009 film)
Macabre (also known as Rumah Dara or Dara) is a 2009 Indonesian slasher film by The Mo Brothers. The film tells the story of a group of friends headed to the airport who meet a woman claiming to have been robbed and needs a ride home, which begins a dark turn of events. The film is based on 2007 short film Dara.
Juan Antonio Lavalleja
Juan Antonio Lavalleja y de la Torre (June 24, 1784 – October 22, 1853) was an Uruguayan libertador, revolutionary, military general, and political figure. He was born in Minas, in a region now named after him as the Lavalleja Department of Uruguay.

Lavalleja Department
Lavalleja (Spanish pronunciation: [laβaˈʝexa]; locally [laβaˈʒexa, -ʃexa]) is a department of Uruguay. Its capital is Minas. It is located in the southeast of the country, bordered to the north by the department of Treinta y Tres to the east with Rocha, to the south with Canelones and Maldonado, and to the west to Florida.

The department is named in honor of Brigadier Juan Antonio Lavalleja, who had distinguished military and political action in the country's independence.
Enkyō (Edo period)
Enkyō (延享)

was a Japanese era name (年号, nengō; lit. "year name") after Kanpō and before Kan'en.  This period spanned the years from February 1744 through July 1748. The reigning emperors were Sakuramachi-tennō (桜町天皇)  and Momozono-tennō (桃園天皇).

Emperor Momozono
Tōhito (Japanese: 遐仁; 14 April 1741 – 31 August 1762), posthumously honored as Emperor Momozono (桃園天皇, Momozono-tennō), was the 116th emperor of Japan, according to the traditional order of succession. Momozono's reign spanned the years from 1747 until his death in 1762. Momozono's reign was mostly quiet, with only one incident occurring that involved a small number of Kuge who advocated for the restoration of direct Imperial rule. These Kuge were punished by the shōgun, who held de facto power in the country.

Momozono fathered two sons with his one and only lady in waiting, but he died at a young age in 1762. The line of succession fell to Momozono's sister, Princess Toshiko, who became Empress Go-Sakuramachi. Due to the young age of Momozono's sons, she also became empress regent to the future Emperor Go-Momozono until he became of age to rule.
Hartington, Derbyshire
Hartington is a village in the centre of the White Peak area of the Derbyshire Peak District, England, lying on the River Dove which is the Staffordshire border.  According to the 2001 census, the parish of Hartington Town Quarter, which also includes Pilsbury, had a population of 345 reducing to 332 at the 2011 Census.  Formerly known for cheese-making and the mining of ironstone, limestone and lead, the village is now popular with tourists.

Tissington Trail
The Tissington Trail is a bridleway, footpath and cycleway in Derbyshire, England, along part of the trackbed of the former railway line connecting Ashbourne to Buxton.  It takes its name from the village of Tissington, which it skirts. Opened in 1971, and now a part of the National Cycle Network, it stretches for 13 miles (21 km) from Parsley Hay (53°10′14″N 1°46′58″W﻿ / ﻿53.1706°N 1.7828°W﻿ / 53.1706; -1.7828﻿ (Tissington Trail (Parsley Hay trailhead))) in the north to Ashbourne (53°01′11″N 1°44′23″W﻿ / ﻿53.0196°N 1.7397°W﻿ / 53.0196; -1.7397﻿ (Tissington Trail (Ashbourne trailhead))) in the south.
Christer Sandelin
Christer Eric Sandelin (born 5 November 1961) is a Swedish singer, songwriter and musician. He has been a part of two groups. In 1978, he was in the Swedish group Freestyle with Tommy Ekman, Joakim Hagleitner, Gigi Hamilton, Diane Söderholm and Anders Uddbergand, and after the break-up of the band in 1983, he continued with Ekman and Hamilton to form the Swedish band trio Style.

In 1989, he started his solo career with his debut album Luften darrar and has had a number of albums. He has also produced for a number of artists Lars Vegas trio and the duos Ronny och Ragge, Rob'n'Raz, Antique and The Graaf Sisters (Magdalena Graaf and Hannah Graaf) and singer Vicki Benckert.

He also continued to cooperate extensively with Tommy Ekman including writing and producing together and in their joint album I Stero and the joint single "Singlar (oh oh)".

The Graaf Sisters
The Graaf Sisters, or Graaf, consists of two Swedish glamour models by the name of Hannah and Magdalena Graaf. The two earned notoriety for appearing in men's magazines together. In 1998, they both gave up glamour modeling and established the pop group named, Graaf. The group is best known for their hit, "You Got What I Want".
Kirby, Wyoming
Kirby is a town in Hot Springs County, Wyoming, United States.

The town was established as a coal town in 1907 alongside the nearby camps of Crosby and Gebo.

The population was 76 at the 2020 census. The town is home to Wyoming Whiskey, the state's first whiskey distillery, and was the only one in the state until 2017. Wyoming Whiskey began production in 2009 in a facility constructed by the General Steel Corporation.

Hot Springs County, Wyoming
Hot Springs County is a county in the U.S. state of Wyoming. As of the 2024 estimates, the population was 4,625, making it the second-least populous county in Wyoming. Its county seat is Thermopolis. The county is named for the hot springs located in Hot Springs State Park.
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.

A Mathematician's Apology
A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy which defends the pursuit of mathematics for its own sake. Central to Hardy's "apology" – in the sense of a formal justification or defence (as in Plato's Apology of Socrates) – is an argument that mathematics has value independent of its applications. Hardy located this value in what he called the beauty of mathematics and gave some examples of and criteria for mathematical beauty. The book also includes a brief autobiography which gives insight into the mind of a working mathematician.
Lust for Life (1956 film)
Lust for Life is a 1956 American biographical film about the life of the Dutch painter Vincent van Gogh, based on the 1934 novel of the same title by Irving Stone which was adapted for the screen by Norman Corwin.

It was directed by Vincente Minnelli and produced by John Houseman. The film stars Kirk Douglas as Van Gogh, James Donald as his brother Theo, with Pamela Brown, Everett Sloane, and Anthony Quinn. Douglas won the Golden Globe Award for Best Actor in a Motion Picture – Drama and the New York Film Critics Circle Award for Best Actor for his performance, while Quinn won the Academy Award for Best Supporting Actor.

Theo van Gogh (art dealer)
Theodorus "Theo" van Gogh (Dutch: [teːjoːˈdoːrʏs ˈteːjoː vɑŋ ˈɣɔx]; 1 May 1857 – 25 January 1891) was a Dutch art dealer and a younger brother of Vincent van Gogh. His support of his older brother's artistic ambitions and well-being allowed Vincent to devote himself entirely to painting. As an art dealer, Van Gogh played a crucial role in introducing contemporary French art to the public.

Van Gogh died at the age of 33, six months after his brother's death at age 37. Van Gogh owned almost all of his brother's artwork. His widow, Johanna van Gogh-Bonger, worked to promote the work of Vincent and keep the memory of her husband alive. In 1914, Van Gogh's remains were buried next to those of his brother Vincent.
Scientific-Humanitarian Committee
The Scientific-Humanitarian Committee (German: Wissenschaftlich-humanitäres Komitee, WhK) was a transnational advocacy group and civil rights organization founded by Magnus Hirschfeld in Berlin in May 1897, to campaign for the legal rights and social recognition of lesbian, gay, bisexual, and transgender (LGBT) people, and against their institutionalized discrimination and persecution in Western societies. It was the first LGBT rights organization in history. The motto of the organization was Per scientiam ad justitiam ("Through science to justice"), and the committee included representatives from various professions. The committee's membership peaked at about 700 people. In 1929, Kurt Hiller took over as chairman of the group from Hirschfeld. At its peak, the WhK had branches in approximately 25 cities in Weimar Germany, the Republic of Austria, and the Netherlands.

LGBTQ rights organization
LGBTQ rights organizations are non-governmental civil rights, health, and community organizations that promote the civil and human rights and health of sexual minorities, and to improve the LGBTQ community.
Goldbach, Zurich
Goldbach is part of the municipality of Küsnacht in the district of Meilen in the canton of Zürich in Switzerland.  Goldbach is located north of Küsnacht proper, south and west of Zollikon, and on the Goldküste (Gold Coast) of Lake Zürich.

The Küsnacht-Goldbach railway station is 12–14 minutes from downtown Zurich via the S6 and S16 S-Bahn train lines.

Goldbach is home to the Goldbach Center and Goldbach Media AG.

47°16′04″N 8°53′26″E﻿ / ﻿47.2679°N 8.8905°E﻿ / 47.2679; 8.8905

Küsnacht Goldbach railway station
Küsnacht Goldbach is a railway station in Switzerland, situated near the eastern bank of Lake Zurich (Goldcoast) in the village of Goldbach, which is itself in the municipality of Küsnacht. The station is on the Lake Zurich right bank railway line. It is located within fare zone 140 of the Zürcher Verkehrsverbund (ZVV).

It is one of four railway stations in the municipality of Küsnacht, the other being Küsnacht ZH, located on the same line, and Forch and Neue Forch, both located on the Forch Railway line.
Sääre, Pärnu County
Sääre is one of the four villages on the island of Kihnu, in southwestern Estonia. Administratively it belongs to Kihnu Parish, Pärnu County. The village is situated in the northern side of the island. In 2000, Sääre had a population of 137.

Kihnu Airfield is located in Sääre.

Kihnu Parish
Kihnu Parish (Estonian: Kihnu vald) is a rural municipality of Estonia, in Pärnu County. The parish covers the 16.88 km² area of Kihnu island, making it one of the smallest parishes in Estonia.  As of 2010, Kihnu Parish had an estimated population of 489.  In 2003, UNESCO named Kihnu Island's culture as a Masterpiece of the Oral and Intangible History of Humanity, placing the island on the organization's Intangible Cultural Heritage list.
The Magnificent Yankee (1950 film)
The Magnificent Yankee is a 1950 American biographical film directed by John Sturges and starring Louis Calhern, Ann Harding, Eduard Franz and Philip Ober. Calhern had created the role of Holmes in the original Broadway production.

The screenplay was adapted by Emmet Lavery from his 1946 play of the same title, which had been adapted from the 1942 book Mr. Justice Holmes by Francis Biddle. The story examines the life of Supreme Court justice Oliver Wendell Holmes Jr.

Francis Biddle
Francis Beverley Biddle (May 9, 1886 – October 4, 1968) was an American lawyer and judge who was the United States Attorney General during World War II. He also served as the primary American judge during Nuremberg trials following World War II and a United States circuit judge of the Court of Appeals for the Third Circuit.
Maserati Ghibli (M157)
The Maserati Ghibli (Tipo M157) is an executive car produced by Italian automobile manufacturer Maserati. The car was unveiled to the public at the 2013 Shanghai Motor Show. The Ghibli ended production at the end of 2023.

Executive car
Executive car is a British term for a large car, and is considered equivalent to the European E-segment and American full-size classifications. Executive cars are larger than compact executive cars (and the non-luxury equivalent mid-size cars), but smaller than luxury saloons / full-size luxury sedans.

The term has also been adopted by Euro NCAP, a European organization founded to test car safety.
Spire City Ghost Hounds
The Spire City Ghost Hounds are an inactive professional baseball team based in Frederick, Maryland, that played in 2023. The franchise competed in the South Division of the Atlantic League of Professional Baseball and played home games at Nymeo Field at Harry Grove Stadium, sharing the ballpark with the Frederick Keys. Following the 2023 season, the team has been on hiatus.

Frederick, Maryland
Frederick is a city in and the county seat of Frederick County, Maryland, United States. Frederick's population was 78,171 people as of the 2020 census, making it the second-largest incorporated city in Maryland behind Baltimore. It is a part of the Washington metropolitan area and the greater Washington–Baltimore combined statistical area.

The city is located at an important crossroads at the intersection of a major north–south Native American trail and east–west routes to the Chesapeake Bay, both at Baltimore and what became Washington, D.C., and across the Appalachian Mountains to the Ohio River watershed.

Frederick is home to Frederick Municipal Airport (IATA: FDK), which accommodates general aviation, and Fort Detrick, a U.S. Army bioscience and communications research installation and Frederick County's largest employer.
Ferenc Márton
Ferenc Márton (15 December 1884 – 8 June 1940) was a Hungarian painter and graphic artist born in Csíkszentgyörgy (now Ciucsângeorgiu, Romania). He was a student of Bertalan Székely and the teacher of Adrienn Henczné Deák.

Ciucsângeorgiu
Ciucsângeorgiu (Hungarian: Csíkszentgyörgy [ˈt͡ʃiːksɛɲɟørɟ]) is a commune in Harghita County, Romania. It is composed of nine villages: Armășeni (Csíkménaság), Armășenii Noi (Ménaságújfalu), Bancu (Csíkbánkfalva), Ciobăniș (Csobányos), Ciucsângeorgiu, Cotormani (Kotormány), Eghersec (Egerszék), Ghiurche (Gyürke), and Potiond (Pottyond).
Sywell Aerodrome
Sywell Aerodrome (IATA: ORM, ICAO: EGBK) is the local aerodrome serving the towns of Northampton, Wellingborough, Kettering and Rushden, as well as wider Northamptonshire, England. The aerodrome is located 5 nautical miles (9.3 km; 5.8 mi) northeast of Northampton and was originally opened in 1928 on the edge of Sywell village.

The aerodrome caters for private flying, flight training and corporate flights. There is a fixed-wing flying school, a microlight school and a helicopter school. The 1930s Art Deco hotel (built in 1934 as the Northamptonshire Aero Club clubhouse) has bar and restaurant facilities. Aviation related industries and businesses are also located at the aerodrome. A viewing area is provided for aircraft spotters where the airfield memorial is located. The Pilots' Mess cafe is also located on site and the large Hangar One venue hosts many events throughout the year.

Kettering
Kettering is a market and industrial town in the North Northamptonshire district of Northamptonshire, England. It lies 45 miles (72 km) west of Cambridge, 31 miles (50 km) south-west of Peterborough, 28 miles (45 km) south-east of Leicester and 15 miles (24 km) north-east of Northampton; it is west of the River Ise, a tributary of the River Nene. The name means "the place (or territory) of Ketter's people (or kinsfolk)".

At the 2021 census, Kettering had a population of 63,150. It is part of the East Midlands, along with the rest of Northamptonshire.
Big Bend High School
Big Bend High School is a public K-12 school located in unincorporated Brewster County, Texas, United States, adjacent to the Study Butte census-designated place, and with a Terlingua postal address. Originally a high school, it now serves as the only school in the Terlingua Common School District and is classified as a 1A school by the UIL. For the 2024–2025 school year, the school was given an "F" by the Texas Education Agency.

In addition to the Terlingua CSD area, Big Bend High also serves high school students from San Vicente Independent School District, based at Big Bend National Park. San Vicente itself does not have enough of a taxation base, as of 1997, to establish its own high school.

Study Butte, Texas
Study Butte (/ˈstjuːdi ˌbjuːt/ STEW-dee BEWT) is a census-designated place (CDP) in Brewster County, Texas, United States. The population was 200 at the 2020 census, down from 233 at the 2010 census. At the 2000 census, the area was part of the Study Butte-Terlingua CDP.
Sacroiliitis
Sacroiliitis is a condition caused by inflammation within the sacroiliac (SI) joint, where the base of the spine (called the sacrum), and the pelvis (called the ilium), connect. The term "sacroiliitis" combines the words sacrum, ilium, and the Latin term "itis", which denotes inflammation.

Inflammation in the SI joint can develop through several different processes. It is a feature of spondyloarthropathies, such as axial spondyloarthritis (including ankylosing spondylitis), psoriatic arthritis, reactive arthritis or arthritis related to inflammatory bowel diseases, including ulcerative colitis or Crohn's disease. It is also the most common presentation of arthritis from brucellosis. Problems with the SI joint are in some cases caused by injury in childbirth, other injury, a congenital condition, or a viral or bacterial infection.

Axial spondyloarthritis
Axial spondyloarthritis (also often referred to as axSpA) is a chronic, immune-mediated disease predominantly affecting the axial skeleton (sacroiliac joints and spine). The term itself is an umbrella term characterizing a diverse disease family united by shared clinical and genetic features, such as the involvement of the axial skeleton. The term axial spondyloarthritis was introduced in 2009, and has to some extent replaced the older, narrower diagnosis of ankylosing spondylitis.
James Lillywhite's Cricketers' Annual
James Lillywhite's Cricketers' Annual was a cricket annual edited by Charles W. Alcock, the secretary of Surrey County Cricket Club, between 1872 and 1900. It is generally referred to as "Red Lillywhite" because of the colour of the cover. It was published by James Lillywhite, Frowd & Co., and sold for 1s.

From the 1876 edition it included a frontispiece, which was an actual photograph affixed into the annual.

The 1883 edition includes a tribute to James Lillywhite senior, who was "the brain which devised the conception of the Annual" and who had died in 1882.

James Lillywhite's Cricketers' Annual incorporated John Lillywhite's Cricketer's Companion from 1886 on, after the latter ceased separate publication in 1885.

Charles W. Alcock
Charles William Alcock (2 December 1842 – 26 February 1907) was an English sportsman, administrator, author and editor. He was a major instigator in the development of both international football and cricket, as well as being the creator of the FA Cup.
Northeast League Aces
The Northeast League Aces (also simply referred to as The Aces) were a baseball traveling team in the Northeast League in the 2004 season to replace the Allentown Ambassadors.

The Ambassadors' roster was dispersed around the league, and the Aces were forced to sign free agents to form a team to compete. They finished the first half of the season in last place in the Northeast League South Division, but rebounded in the second half to finish second, albeit a distant second, behind the eventual league champion New Jersey Jackals.

For the inaugural Can-Am League season in 2005, the Aces were disbanded and replaced by a permanent team in Worcester, Massachusetts.

The Aces used the logo of the then-defunct Alexandria Aces for their lone year of existence. (The logo was later used by the new incarnation of the Alexandria Aces, who were reformed in 2006 and played until 2013 in the Texas Collegiate League.)

Can–Am League
The Canadian American Association of Professional Baseball, commonly known as the Can-Am League, was a professional baseball league with teams in Eastern Canada and Northeastern United States. Founded in 2005 in Dayton, Ohio, the league was formed as a reorganization of the Northeast League following the 2004 season.

The Can-Am League operated in cities not directly served by Major or Minor League teams and was not affiliated with either. Though a separate entity, the league shared a commissioner, president, and director of umpires with the American Association of Professional Baseball. The league was headquartered in Dayton, Ohio.

The league ceased operations after the 2019 season, with five of the remaining six teams joining the Frontier League.