hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Center (group theory)
In abstract algebra, the center of a group G is the set of elements that commute with every element of G. It is denoted Z(G), from German Zentrum, meaning center. In set-builder notation,

Z(G) = {z ∈ G | ∀g ∈ G, zg = gz}.

The center is a normal subgroup, , and also a characteristic subgroup, but is not necessarily fully characteristic. The quotient group, G / Z(G), is isomorphic to the inner automorphism group, Inn(G).

A group G is abelian if and only if Z(G) = G. At the other extreme, a group is said to be centerless if Z(G) is trivial; i.e., consists only of the identity element.

The elements of the center are central elements.

Order (group theory)
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element a of a group, is thus the smallest positive integer m such that am = e, where e denotes the identity element of the group, and am denotes the product of m copies of a. If no such m exists, the order of a is infinite.

The order of a group G is denoted by ord(G) or |G|, and the order of an element a is denoted by ord(a) or |a|, instead of  where the brackets denote the generated group.

Lagrange's theorem states that for any subgroup H of a finite group G, the order of the subgroup divides the order of the group; that is, |H| is a divisor of |G|. In particular, the order |a| of any element is a divisor of |G|.
Cuscatlán Department
Cuscatlán (Spanish pronunciation: [kuskaˈtlan]) is a department of El Salvador, located in the center of the country. With a surface area of 756.19 square kilometres (291.97 sq mi), it is El Salvador's smallest department. Cuscatlán or Cuzcatlán was the name the original inhabitants of the Western part of the country gave to most of the territory that is now El Salvador. In their language it means "land of precious jewels". It was created on 22 May 1835. Suchitoto was the first capital of the department but on 12 November 1861, Cojutepeque was made the capital. It is known in producing fruits, tobacco, sugar cane, and coffee among other items. The department is famous for its chorizos from the city of Cojutepeque.

La Paz Department (El Salvador)
La Paz (Spanish pronunciation: [la pas]) is a department of El Salvador in the south central area of the country. The capital is Zacatecoluca. La Paz has an area of 1,228 km2. The department was created in 1852. There are various caves containing rock writing. The department has a church in Zacatecoluca where the Independence Hero Dr Jose Simeon Cañas y Villacorta was born. He was known as "The Liberator of the Slaves in Central America". In 1833, Anastasio Aquino, an indigenous person, proclaimed himself as "The Emperor of the Nonualcos".
Mattias Norström
Erik Johan Mattias "Notan" Norström (born 2 January 1972) is a Swedish former professional ice hockey defenceman, currently working for the AIK organization.  Norström began his National Hockey League career with the New York Rangers.  However, he is most noted for his ten seasons as a member of the Los Angeles Kings for whom he served as team captain from 2001–2007; he was the team's first non-North American-born captain and would represent the Kings twice in the NHL All Star Game. Norström played the final season of his NHL career for the Dallas Stars.

Michael Nylander
Michael Gunnar Nylander (born 3 October 1972) is a Swedish former professional ice hockey centre and coach. He played for fifteen seasons in the NHL, and represented the Swedish national team in multiple Olympics and World Championships.
Adam West
William West Anderson (September 19, 1928 – June 9, 2017), known professionally as Adam West, was an American actor. He portrayed Batman in the 1960s ABC series of the same name and its 1966 theatrical feature film, reprising the role in various media until 2017. Having made his film debut in the 1950s, West starred opposite Chuck Connors in Geronimo (1962) and The Three Stooges in The Outlaws Is Coming (1965). He also appeared in the science fiction film Robinson Crusoe on Mars (1964).

He voiced parodied versions of himself in the animated television sitcoms Johnny Bravo (1997, 2004), The Fairly OddParents (2003–2008), The Simpsons (1992, 2002), and Family Guy (2000–2017). In the latter, he played Mayor Adam West between the second and seventeenth seasons. He received a television star on the Hollywood Walk of Fame in 2012.

Fred Tatasciore
Fred Tatasciore (/ˈtætəʃɔːr/ TAT-ə-shor, Italian: [tataʃˈʃoːre], born June 15, 1967) is an American voice actor who has provided voices in animated and live-action films, television shows, and video games. He is known for voicing the Hulk, Volstagg, and Beast in various Marvel media and Solomon Grundy and Bane in various DC media. Other characters he has voiced include Yosemite Sam, Taz, Michigan J. Frog, Soldier: 76, Shao Kahn, Dingodile and Kakuzu. From 2021 to 2024, he starred as the title character in the adult animated series Hit-Monkey.
Kansas State University
Kansas State University (KSU, Kansas State, or K-State) is a public land-grant research university with its main campus in Manhattan, Kansas, United States. It was opened as the state's land-grant college in 1863 and was the first public institution of higher learning in the state of Kansas.  It is governed by the Kansas Board of Regents.

The university is classified among "R1: Doctoral Universities – Very high research activity". Kansas State's academic offerings are administered through nine colleges, including the College of Veterinary Medicine and the College of Technology and Aviation in Salina. Graduate degrees offered include 65 master's degree programs and 45 doctoral degrees.

Branch campuses are in Salina and Olathe. The Kansas State University Salina Aerospace and Technology Campus is home to the College of Technology and Aviation. The Olathe Innovation Campus has a focus on graduate work in research bioenergy, animal health, plant science and food safety and security.

Jerome Tang
Jerome Tang (born October 7, 1966) is a Trinidadian-American college basketball coach who was most recently the head coach at  Kansas State University. He had previously been an assistant coach under Scott Drew from 2003 to 2022 at Baylor, where the Bears won the 2021 NCAA Championship.
Peloponnese
The Peloponnese, Peloponnesus, or Morea, is a peninsula and geographic region in Southern Greece, and the southernmost region of the Balkans. It is connected to the central part of the country by the Isthmus of Corinth land bridge, which separates the Gulf of Corinth from the Saronic Gulf. From the late Middle Ages until the 19th century, the peninsula was known as the Morea, a name still in colloquial use in its demotic form.

The peninsula is divided among three administrative regions: most belong to the Peloponnese region, with smaller parts belonging to the West Greece and Attica regions.

Bassae
Bassae (Latin: Bassae, Ancient Greek: Βάσσαι – Bassai, meaning "little vale in the rocks") is an archaeological site in Oichalia, a municipality in the northeastern part of Messenia, Greece. In classical antiquity, it was part of Arcadia. Bassae lies near the village of Skliros, northeast of Figaleia, south of Andritsaina and west of Megalopolis. It is famous for the well-preserved mid- to late-5th century BC Temple of Apollo Epicurius.

Although this temple is geographically remote from major polities of ancient Greece, it is one of the most studied ancient Greek temples because of its multitude of unusual features. Bassae was the first Greek site to be inscribed on the World Heritage List, in 1986.
Colette Mann
Colette Mann (born 17 February 1950) is an Australian actress, singer, TV and radio presenter, choreographer, writer and media personality, who has been in the entertainment industry for over 50 years. She is known for her roles in Prisoner (1979–1984) as Doreen May Anderson Burns, and Neighbours (2012–2022) as Sheila Canning.

Morgana O'Reilly
Morgana O'Reilly (born 19 August 1985) is a New Zealand film, television and theatre actress. She has appeared in several theatre productions and created the one-woman play The Height of the Eiffel Tower, which she performed at the Edinburgh Fringe Festival in 2014. O'Reilly played Lynn Matthews in the biographical television film Billy and starred as Kylie Bucknell in the horror-comedy Housebound. She has made appearances in Nothing Trivial, Sunny Skies, This is Littleton. O'Reilly played Naomi Canning in Neighbours from 2014 until 2015. She made guest appearances in 2020 and 2022. She starred in sitcom Mean Mums and joined the cast of Wentworth as Narelle Stang in 2019. O'Reilly and her husband Peter Salmon created the comedy-thriller INSiDE, which won the International Emmy Award for Best Short-Form Series in 2021.
EMM386
EMM386 is the expanded memory manager of Microsoft's MS-DOS, IBM's PC DOS, Digital Research's DR-DOS, and Datalight's ROM-DOS which is used to create expanded memory using extended memory on Intel 80386 CPUs. There also is an EMM386.EXE available in FreeDOS.

386MAX
386MAX (originally 386 to the Max, later Qualitas MAX) is a computer memory manager for DOS-based personal computers. It competed with Quarterdeck's QEMM memory manager. It was manufactured by Qualitas.

BlueMax was a special version designed for the IBM PS/2 with ROM compression to get the most of the Upper Memory Blocks.

In 2022, the source code was made available on GitHub, and released under the GNU GPL v3 license by Bob Smith of Sudley Place Software. It joined other tools that Smith had originally written at Qualitas which had their source code released in 2012:

DPMIONE, a DPMI 1.0 host component

386SWAT, a protected-mode debugger

QLINK, a linker tool written to handle 32-bit data types, in support of the 386SWAT program
B. Brian Blair
Brian Leslie Blair (born January 12, 1957) is an American former professional wrestler. He is best known for his appearances with the World Wrestling Federation (WWF) under the ring name B. Brian Blair as one half of the tag team The Killer Bees in the 1980s.

Ken Patera
Kenneth Wayne Patera (born November 6, 1942) is an American retired professional wrestler, Olympic weightlifter, and strongman competitor. He was well known in the World Wrestling Federation from 1976 to 1981, 1984 to 1985 and 1987 to 1988 and American Wrestling Association.
Louis XIV's East India Company
Louis XIV's East India Company (French: Compagnie des Indes orientales) was a joint-stock company founded in the Kingdom of France in August 1664 to engage in trade in India and other Asian lands, complementing the French West India Company (French: Compagnie des Indes occidentales) created three months before. It was one of several successive enterprises with similar names, a sequence started with Henry IV's first French East Indies Company in 1604 and continued with Cardinal Richelieu's Compagnie d'Orient in 1642. Planned by Jean-Baptiste Colbert to compete with the English East India Company and Dutch East India Company,: 24  it was chartered by King Louis XIV for the purpose of trading in the Eastern Hemisphere.

Louis XIV's company became insolvent and was reorganized in 1685, and was again bankrupt in 1706. In 1719, what remained of it was acquired by John Law's Company, which in 1723 became the French Indies Company active during much of the 18th century.

Chandannagar
Chandannagar (Bengali pronunciation: [t͡ʃɔn.d̪ɔn.nɔ.ɡoɾ]), also known by its former names Chandernagor (French pronunciation: [ʃɑ̃.dɛʁ.na.ɡɔʁ]) and Chandernagore, is a city in the Hooghly district in the Indian state of West Bengal. It is headquarter of the Chandannagore subdivision and is a part of the area covered by Kolkata Metropolitan Development Authority (KMDA).

Located on the western bank of Hooghly River, the city was one of the five French Settlements in India. Indo-French architecture is seen in the colonial bungalows, most of which are in a dilapidated state.
Tau6 Eridani
Tau6 Eridani, Latinized from τ6 Eridani, is a single star in the equatorial constellation of Eridanus, located near the constellation border with Fornax. It has a yellow-white hue with an apparent visual magnitude of 4.22, which is bright enough to be seen with the naked eye. Based upon parallax measurements, the distance to this star is around 57.5 light years. It is drifting further away with a radial velocity of +8 km/s.

The spectrum of Tau6 Eridani matches a stellar classification of F5IV-V, indicating it is an F-type star that shows traits of both a main sequence star and a subgiant. It has an estimated 140% of the Sun's mass and 1.73 times the radius of the Sun. The star is radiating 5.29 times the luminosity of the Sun at an effective temperature of 6,651 K, and it does not display any surface magnetic activity. The star has been examined for infrared excess emission that could indicate the presence of circumstellar matter, but none has been detected.

Tau7 Eridani
Tau7 Eridani is a solitary star in the constellation Eridanus. It is visible to the naked eye with an apparent visual magnitude of 5.235. Using the parallax method, the distance to this star can be estimated as around 251 light years.

This is an A-type main sequence star with a stellar classification of A3 Vs, where the 's' indicates it has narrow absorption lines. It may be a chemically peculiar Am star, which means it displays unusual abundances of certain elements in its surface layers. Tau7 Eridani appears to be a low amplitude variable that displays slight fluctuations in luminosity over a period of 7.17 days. It is slowly rotating with a projected rotational velocity of 18 km/s, and is around 387 million years old.
Frederick William, the Great Elector
Frederick William (German: Friedrich Wilhelm; 16 February 1620 – 29 April 1688) was Elector of Brandenburg and Duke of Prussia, thus ruler of Brandenburg-Prussia, from 1640 until his death in 1688. A member of the House of Hohenzollern, he is popularly known as "the Great Elector" (der Große Kurfürst) because of his military and political achievements. Frederick William was a staunch pillar of the Calvinist faith, associated with the rising commercial class. He saw the importance of trade and promoted it vigorously. His shrewd domestic reforms gave Prussia a strong position in the post-Westphalian political order of Northern-Central Europe, setting up Prussia for elevation from duchy to kingdom, achieved under his son and successor.

County of Ravensberg
The County of Ravensberg (German: Grafschaft Ravensberg) was a historical county of the Holy Roman Empire. Its territory was in present-day eastern Westphalia, Germany, at the foot of the Osning or Teutoburg Forest.
Operation Barga
Operation Barga was a land reform movement, throughout rural West Bengal for recording the names of sharecroppers (bargadars) while avoiding the time-consuming method of recording through the settlement machinery. It bestowed on the bargadars, the legal protection against eviction by the landlords (jotedars), and entitled them to the due share of the produce. Operation Barga was launched in 1978 and concluded by the mid-1980s. Introduced in 1978, and given legal backing in 1979 and 1980, Operation Barga became a popular but controversial measure for land reforms. The ultimate aim of these land reforms was to facilitate the conversion of the state's bargadars into landowners, in line with the Directive Principles of State Policy of the Indian Constitution. To date, Op Barga has recorded the names of approximately 1.5 million bargadars. Since then, it has been marked as one of the most successful land reforms programs in India.

Left Front (West Bengal)
The Left Front is an alliance of left-wing political parties in the Indian state of West Bengal. It was formed in January 1977, the founding parties being the Communist Party of India (Marxist), All India Forward Bloc, the Revolutionary Socialist Party, the Marxist Forward Bloc, the Revolutionary Communist Party of India and the Biplobi Bangla Congress. Other parties joined in later years, most notably the Communist Party of India.

The Left Front ruled the state of West Bengal for 34 years in seven consecutive terms 1977–2011, five with Jyoti Basu as Chief Minister and two under Buddhadev Bhattacharya. The CPI(M) is the dominant force in the alliance. In the 2011 West Bengal Legislative Assembly election the Left Front failed to gain a majority of seats and left office. As of 2016 Biman Bose is the Chairman of the West Bengal Left Front Committee.
UB-Barça
Club Bàsquet Femení Universitari de Barcelona–FC Barcelona was a Spanish Catalan women's basketball team. Initially named CBF Universitari de Barcelona, belonging just to the Universitat de Barcelona, it later became part of the FC Barcelona family. They used to have four base teams: junior, cadet, infantil and infantil'91.

UB-Barça was one of the most successful teams in the Spanish League in the first half of the 2000s, winning the championship in 2003 and 2005. However, in 2007 FC Barcelona retired its sponsorship, and the club, not being able to face its expenses, was relegated and disbanded.

Notable former players include Marta Fernández, Helen Luz, Razija Mujanović and Érika de Souza.

Ros Casares Godella
Ros Casares Godella was a professional women's basketball team based in Godella, Spain. It played in the Liga Femenina de Baloncesto between 1996 and 2012, when it resigned to play in EuroLeague and Spanish League. It continued playing in Primera División Femenina, third tier of Spanish women's basketball, until 2014 when the club was integrated in Valencia Basket as its women's section.
57th (West Middlesex) Regiment of Foot
The 57th (West Middlesex) Regiment of Foot was a regiment of line infantry in the British Army, raised in 1755. Under the Childers Reforms it amalgamated with the 77th (East Middlesex) Regiment of Foot to form the Middlesex Regiment in 1881.

39th (Dorsetshire) Regiment of Foot
The 39th (Dorsetshire) Regiment of Foot was an infantry regiment of the British Army, raised in 1702. Under the Childers Reforms it amalgamated with the 54th (West Norfolk) Regiment of Foot to form the Dorsetshire Regiment in 1881.
Lyon County, Iowa
Lyon County is the most northwestern county of the U.S. state of Iowa. As of the 2020 census, the population was 11,934. The county seat is Rock Rapids.

Lyon County is named in honor of Brigadier General Nathaniel Lyon, who served in the Mexican–American War and the Civil War. He was killed at the Battle of Wilson's Creek, Missouri, on August 10, 1861, after which the county was named for him. The county's name was originally Buncombe County, but was changed by the state legislature on September 11, 1862.

Buena Vista County, Iowa
Buena Vista County (/ˈbjuːnə ˈvɪstə/; Spanish pronunciation: [ˈbwena ˈβista]) is a county located in the U.S. state of Iowa. As of the 2020 census, the population was 20,823. Its county seat is Storm Lake. The county is named for the final victory of Field General Zachary Taylor in the Mexican–American War.

Buena Vista County comprises the Storm Lake, IA Micropolitan Statistical Area.
Pine Grove, Schuylkill County, Pennsylvania
Pine Grove is a borough in Schuylkill County, Pennsylvania,  United States. As of the 2020 census, the borough population was 2,054.

Pine Grove Area School District, serving students from three municipalities and multiple surrounding townships, is located in the borough.

Union Canal (Pennsylvania)
The Union Canal was a towpath canal that existed in southeastern Pennsylvania in the United States during the 19th century. First proposed in 1690 to connect Philadelphia with the Susquehanna River, it ran approximately 82 mi from Middletown on the Susquehanna below Harrisburg to Reading on the Schuylkill River.
Delft
Delft (Dutch pronunciation: [ˈdɛl(ə)ft] ⓘ) is a city and municipality in the province of South Holland, Netherlands. It is located between Rotterdam, to the southeast, and The Hague, to the northwest. Together with them, it is a part of both the Rotterdam–The Hague metropolitan area and the Randstad.

Delft is a popular tourist destination in the Netherlands, famous for its historical connections with the reigning House of Orange-Nassau, for its blue pottery, for being home to the painter Jan Vermeer, and for hosting Delft University of Technology (TU Delft). Historically, Delft played a highly influential role in the Dutch Golden Age. In terms of science and technology, thanks to the pioneering contributions of Antonie van Leeuwenhoek and Martinus Beijerinck, Delft can be considered to be the birthplace of microbiology.

Leidschendam-Voorburg
Leidschendam-Voorburg (Dutch pronunciation: [ˌlɛitsə(n)dɑɱˈvoːrbʏr(ə)x] ⓘ) is a municipality in the Western Netherlands, in the province of South Holland, just northeast of The Hague. It had a population of 76,433 in 2021, and covers an area of 35.62 km2 (13.75 sq mi) of which 3.07 km2 (1.19 sq mi) is water.
Lupita D'Alessio
Guadalupe Contreras Ramos (born 10 March 1954), better known as Lupita D'Alessio (Spanish pronunciation: [luˈpita ðaˈlesjo]), is a Mexican singer and actress. She is nicknamed "La Leona Dormida" (title of one of her signature songs, "The sleeping lioness").

Daniela Romo
Teresa Presmanes Corona (born 27 August 1959), known professionally as Daniela Romo, is a Mexican singer, actress and TV hostess. During her career, she has sold 15 million records, making her one of the best-selling Latin music artists.
Superior, Arizona
Superior (Western Apache: Yooʼ Łigai) is a town in northern Pinal County, Arizona, United States, and is the oldest town in the county. According to the 2020 census, the population of the town was 2,407. Superior was founded as a mining town for the Silver King and the later Magma mines; silver was mined at first, and then transitioned to copper.  Currently, exploitation of the huge Resolution Copper deposit is being explored.

U.S. Route 60 in Arizona
U.S. Route 60 (US 60) is an east–west United States Highway within Arizona. The highway runs for 369 miles (594 km) from a junction with Interstate 10 near Quartzsite to the New Mexico state line near Springerville. As it crosses the state, US 60 overlaps at various points: I-17, I-10, SR 77, SR 260, US 191, and US 180. Between Wickenburg and Phoenix, the route is known as the Phoenix–Wickenburg Highway. As an arterial inside the Phoenix metropolitan area it is known as Grand Avenue. When concurrent with Interstates through Downtown Phoenix, the route is known as the Black Canyon Highway from Thomas Road and Grand Avenue to the Durango Curve. From the Durango Curve to the Broadway Curve in Tempe, the route is known as the Maricopa Freeway. From Tempe to Apache Junction, it is known as the Superstition Freeway.
Lgov, Kursk Oblast
Lgov (Russian: Льгов, IPA: [ˈlʲɡof]) is a town in Kursk Oblast, Russia, located on both sides of the Seym river (a tributary of the Desna) 80 kilometers (50 mi) west of Kursk and an equal distance from Hlukhiv, Ukraine. Population as of 2021 was 17,557.

Kurchatov, Russia
Kurchatov (Russian: Курча́тов) is a town in Kursk Oblast, Russia, located on the Seym River 42 kilometers (26 mi) west of Kursk. Population: 40,318 (2021 Census); 42,706 (2010 Census); 45,556 (2002 Census); 41,085 (1989 Soviet census).