hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Commutator subgroup
In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.

The commutator subgroup is important because it is the smallest normal subgroup such that the quotient group of the original group by this subgroup is abelian. In other words,  is abelian if and only if  contains the commutator subgroup of . So in some sense it provides a measure of how far the group is from being abelian; the larger the commutator subgroup is, the "less abelian" the group is.

Abelian group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after the Norwegian mathematician Niels Henrik Abel.

The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified.
Henry Daniel Sinclair
Henry Daniel Sinclair (1818 – 17 March 1868) was an explorer and co-founder of Bowen, Queensland, Australia. Captain Sinclair led an expedition which resulted in the naming of Port Denison (the port of Bowen) in 1859 in the cutter Santa Barbara.

Bowen, Queensland
Bowen is a coastal town and locality in the Whitsunday Region, Queensland, Australia. In the 2021 census, the locality of Bowen had a population of 11,205 people.

The locality contains two other towns:

Heronvale (20°06′25″S 148°17′36″E﻿ / ﻿20.107°S 148.2933°E﻿ / -20.107; 148.2933﻿ (Heronvale, Queensland))

Merinda (20°00′59″S 148°09′53″E﻿ / ﻿20.0164°S 148.1647°E﻿ / -20.0164; 148.1647﻿ (Merinda, Queensland)).

The Abbot Point coal shipping port is also within the locality (19°52′54″S 148°04′46″E﻿ / ﻿19.8816°S 148.0795°E﻿ / -19.8816; 148.0795﻿ (Abbot Point)).
Jai Bhim
Jai Bhim (alternatively spelled Jay Bhim or Jai Bheem; transl. "Victory for Bhim", "Long live Bhim" or "Hail Bhim"; pronounced [d͡ʒəj bʱiːm] or [d͡ʒɛː bʱiːm]) is a slogan and greeting used by followers of B. R. Ambedkar, an Indian politician, social reformer and first Law and Justice Minister of India. It refers to Ambedkar's given name Bhimrao. In 1935, Jai Bhim was conceived and developed by Babu L. N. Hardas (1904–1939), a staunch follower of Ambedkar, and the secretary of Samata Sainik Dal. However, its origin is obscure and may date as far back as 1818, well before Ambedkar's birth.

Jai Bhim is also called as a slogan by some political parties like the Bahujan Samaj Party (BSP), Republican Party of India (RPI).

L. N. Hardas
Hardas Laxmanrao Nagrale (6 January 1904 – 12 January 1939), popularly known as Babu Hardas, was an Indian Dalit leader, politician and social reformer. He was an ardent follower of B. R. Ambedkar and was pioneer of the practice of exchanging the greeting Jai Bhim amongst the Dalits.  He was also a prominent labour leader in the Central Province and was the general secretary of the Independent Labour Party in the province. Hardas was also the first Member of the Legislative Assembly to be elected from Nagpur Kamptee constituency in 1937.
Ruddy duck
The ruddy duck (Oxyura jamaicensis) is a species of duck in the family Anatidae. The ruddy duck is one of six species within the stiff-tailed ducks (genus Oxyura). Stiff-tailed ducks occupy heavily vegetated habitats in North and South America as well as the British Isles, France, and Spain. In the 1940s, the ruddy duck was introduced to the United Kingdom, where it has since established a growing population. Outside the Americas, the ruddy duck is considered a highly invasive species, prompting many countries to initiate culling projects to eradicate it from the native ecosystem.

The generic name is derived from Ancient Greek oxus meaning "sharp", and oura meaning "tail". The specific name jamaicensis means "from Jamaica". The ruddy duck has also been nicknamed "butterball", a term used to describe an individual that is somewhat fat, due to its short and stout stature making activities like flying and walking upright awkward.

Anatidae
The Anatidae are the biological family of water birds that includes ducks, geese, and swans. The family has a cosmopolitan distribution, occurring on all the world's continents except Antarctica. These birds are adapted for swimming, floating on the water surface, and, in some cases, diving in at least shallow water. The family contains around 174 species in 43 genera (the magpie goose is no longer considered to be part of the Anatidae and is now placed in its own family, Anseranatidae).

They are generally herbivorous and are monogamous breeders. A number of species undertake annual migrations. A few species have been domesticated for agriculture, and many others are hunted for food and recreation. Five species have become extinct since 1600, and many more are threatened with extinction.
Iron Man's armor (Marvel Cinematic Universe)
Tony Stark has worn different versions of the Iron Man armor throughout the Marvel Cinematic Universe (MCU). He has also built armor for James Rhodes (which became the War Machine armor), the Iron Spider suit for Peter Parker, and Pepper Potts' Rescue armor.

The physical armor used in Iron Man (2008) was built by Stan Winston Studios, with the digital version and other visual effects created by Industrial Light & Magic. Further appearances of the armor in the MCU were mainly created through visual effects. Iron Man comic book artist Adi Granov designed the Mark III, with further armors also being inspired by the armors from the comics.

Pepper Potts (Marvel Cinematic Universe)
Virginia "Pepper" Potts is a fictional character in the Marvel Cinematic Universe based on the Marvel Comics character of the same name. Portrayed by Gwyneth Paltrow, she is depicted as Tony Stark's personal assistant and later his love interest, ultimately becoming his wife. In later installments in the MCU, Pepper takes over operation of his company, Stark Industries, as Stark moves on to focus on serving as Iron Man. In later films, Potts assists Stark and the Avengers with her own powered suit Rescue.

As of 2022, Potts has appeared in seven films, most recently in Avengers: Endgame (2019). Alternate versions of Potts also appear in the animated series What If...? (2021).
William Roscoe
William Roscoe (8 March 1753 – 30 June 1831) was a British banker, lawyer and politician. He is best known as one of England's first abolitionists, and as the author of the poem for children The Butterfly's Ball, and the Grasshopper's Feast. In his day he was also respected as a historian and art collector, as well as a botanist and miscellaneous writer. The standard author abbreviation Roscoe is used to indicate this person as the author when citing a botanical name.

Abolitionism in the United Kingdom
Abolitionism in the United Kingdom was the movement in the late 18th and early 19th centuries to end the practice of slavery, whether formal or informal, in the United Kingdom, the British Empire and the world, including ending the Atlantic slave trade. It was part of a wider abolitionism movement in Western Europe and the Americas. It spanned over a century and involved a wide range of activists, politicians, religious groups, and former slaves.

The trade of slaves was abolished throughout the British Empire by 1937, with Nigeria and Bahrain being the last British territories to abolish slavery.
Czechoslovakia at the Olympics
Czechoslovakia first participated at the Olympic Games in 1918, after having competed as Bohemia from 1900 to 1912. The nation sent athletes to compete in every Summer Olympic Games since then, except for the 1984 Games when they were part of the Soviet-led boycott of the 1984 Summer Olympics.
Czechoslovakia has participated in every Winter Olympic Games since the inaugural Games of 1924.

After the dissolution of Czechoslovakia in 1993, the Czech Republic and Slovakia sent independent teams to the Olympics starting in 1994.

Czechoslovak athletes have won a total of 143 medals at the Summer Games, mostly in gymnastics. The nation also won 25 medals at the Winter Games, with ski jumping and ice hockey as the top medal-producing sports.

Bohemia at the Olympics
The Kingdom of Bohemia, an autonomous part of Austria-Hungary until 1918, competed at some of the early modern Olympic Games.  The team made its debut at the 1900 Summer Olympics.  After World War I, Bohemia became part of the new Czechoslovakia, and Bohemian athletes competed for Czechoslovakia at the Olympics.  After the 1992 Summer Olympics and the dissolution of Czechoslovakia into the Czech Republic and Slovakia in 1993, Bohemian athletes competed for the Czech Republic at the Olympics.  If these post-war appearances are counted, Bohemia has missed only three Olympics: the inaugural 1896 Summer Olympics, the 1904 Summer Olympics (the first held outside Europe) and as Czechoslovakia, the 1984 Summer Olympics which were boycotted by the USSR and its satellites.
Charles Wentworth-Fitzwilliam, 5th Earl Fitzwilliam
Charles William Wentworth Fitzwilliam, 5th Earl Fitzwilliam in the peerage of Ireland and 3rd Earl Fitzwilliam in the peerage of Great Britain, (4 May 1786 – 4 October 1857) was a British nobleman and politician. He was president three times of the Royal Statistical Society in 1838–1840, 1847–1849, and 1853–1855; and president of the British Association for the Advancement of Science in its inaugural year (1831–2).

William Fitzwilliam, 4th Earl Fitzwilliam
William Wentworth-Fitzwilliam, 4th Earl Fitzwilliam PC (30 May 1748 – 8 February 1833), styled Viscount Milton until 1756, was a British Whig statesman of the late 18th and early 19th centuries. In 1782 he inherited the estates of his uncle Charles Watson-Wentworth, 2nd Marquess of Rockingham, making him one of the richest people in Britain. He played a leading part in Whig politics until the 1820s.
WNKR
WNKR (106.7 FM) is a commercial radio station licensed to Williamstown, Kentucky, and serving the Cincinnati metropolitan area.  It airs an oldies format and has been owned since its inception by Grant County Broadcasters, Inc., an independent and local company.

WNKR has an effective radiated power (ERP) of 1,800 watts. The transmitter is off U.S. Route 25 in Dry Ridge, Kentucky. Programming is simulcast with WOXY 97.7 FM, licensed to Mason, Ohio.

WOXY (FM)
WOXY (97.7 MHz) is an FM radio station licensed to Mason, Ohio as part of the Cincinnati and Dayton, Ohio markets.  Nicknamed 97.7/106.7/94.5 The Oasis, the station broadcasts an oldies music format.

Originally located in Oxford, Ohio, the station began broadcasting in 1959 as WOXR before changing its call sign to WOXY in 1978. The station became widely known, as 97X, for its successful alternative rock format from 1983 to 2004.
Suresh Joshi
Suresh Hariprasad Joshi (30 May 1921 – 6 September 1986) was an Indian novelist, short-story writer, literary critic, poet, translator, editor and academic in the Gujarati language. Along with his teaching career, he led the modernist movement in Gujarati literature. He was prolific writer and he transformed the field of literary criticism.

Shirish Panchal
Shirish Jagjivandas Panchal (born 7 March 1943) is a Gujarati critic, fiction writer, translator and editor. He won the 2009 Sahitya Akademi Award for Gujarati language for his criticism Vaat Aapanaa Vivechan-ni. He refused the award.
Ned Rifle
Ned Rifle is a 2014 American drama film written and directed by Hal Hartley. It is the third and final film in a trilogy following characters introduced in Hartley's 1997 film Henry Fool and 2006 sequel Fay Grim. Ned Rifle stars Liam Aiken as the title character, reprising his role from the other two films, as well as Aubrey Plaza, Parker Posey, James Urbaniak, and Thomas Jay Ryan.

The film premiered at the 2014 Toronto International Film Festival on September 7, 2014.

The film was released in select theaters and on demand beginning on April 1, 2015.

Fay Grim
Fay Grim is a 2006 espionage thriller film written and directed by Hal Hartley. The film is a sequel to Hartley's 1997 film Henry Fool, and revolves around the title character, played by Parker Posey, the sister of Simon Grim (James Urbaniak).  The plot revolves around Fay's attempt to unravel an increasingly violent mystery in Europe.

Hartley began writing the script in 2002, and filming took place in Europe from January to March 2006. It premiered in September at the 2006 Toronto International Film Festival, and received a theatrical release in the United States on May 18, 2007. The film was shot almost entirely in Dutch angles, meaning the vast majority of shots are framed diagonally, or "tilted".  At the 2007 Sundance Film Festival, Hartley revealed that the two shots in the film's final cut that are not "Dutched" occurred when he and the film crew forgot to tilt the camera.

A sequel, Ned Rifle, was released in 2014.
Air Do
Air Do  is a Japanese regional airline headquartered in Sapporo, Japan. It operates scheduled service between the islands of Honshu and Hokkaido in cooperation with All Nippon Airways, from its hubs at New Chitose Airport in Sapporo and Haneda Airport in Tokyo.

All Nippon Airways
All Nippon Airways (ANA) is a Japanese airline headquartered in Minato, Tokyo. ANA operates services to both domestic and international destinations and is Japan's largest airline, ahead of its main rival Japan Airlines. As of March 2024, the airline has approximately 12,800 employees. The airline joined as a Star Alliance member in October 1999.

In addition to its mainline operations, ANA controls several subsidiary passenger carriers, such as its regional airline ANA Wings, Air Nippon, Air Do (a low-cost carrier operating scheduled service between Tokyo and cities in Hokkaido), Air Japan and Allex Cargo (ANA Cargo – the freighter division operated by Air Japan). Peach Aviation, a low-cost carrier based in Japan, is fully owned by ANA.
Bramwell Booth
William Bramwell Booth, CH (8 March 1856 – 16 June 1929) was a British church and charity leader who was the first Chief of Staff (1881–1912) and the second General of The Salvation Army (1912–1929), succeeding his father, William Booth.

Catherine Booth
Catherine Booth (née Mumford, 17 January 1829 – 4 October 1890) was co-founder of The Salvation Army, along with her husband William Booth. Because of her influence in the formation of The Salvation Army she was known as the 'Mother of The Salvation Army'.
Ed Ra
Edward P. Ra is an American politician from the state of New York. He represents New York's 19th State Assembly district, which includes portions of the towns of Hempstead, North Hempstead and Oyster Bay in Nassau County on Long Island. A Republican, Ra was first elected to the New York State Assembly in 2010. He became the minority leader of the Assembly in February 2026.

Hempstead, New York
The Town of Hempstead is the most populous town in the state of New York. It is the largest of the three towns within Nassau County (alongside North Hempstead and Oyster Bay), located on Long Island, east of Queens. The population was 793,409 at the time of the 2020 census.

It occupies the southwestern part of the county, near the western end of Long Island. A total of 22 incorporated villages (one of which is named Hempstead) are completely or partially within the town.

Hofstra University's campus is located in Hempstead.
Workington Opera House
The Workington Opera House, or The Opera as it was known, is a purpose built theatre located in Workington, Cumbria, England. Originally built as the Queen’s Jubilee Hall & Opera House it was gutted by fire in 1927 and rebuilt with a fine wide auditorium, and Ornamental ceiling with seating for 1200. The theatre has good sightlines and a large stage and currently sits empty after its former use as a bingo hall ended in 2004.

Workington
Workington /ˈwɜːrkɪŋtən/ is a coastal port town and civil parish in the Cumberland district of Cumbria, England. The town is at the mouth of the River Derwent on the west coast, 32 miles (51 km) south-west of Carlisle and 8 miles (13 km) north-east of Whitehaven. At the 2021 census the parish had a population of 25,448 and the built up area had a population of 21,275.
Chōsokabe Motochika
Chōsokabe Motochika (長宗我部 元親; 1539 – July 11, 1599) was a daimyō in Japanese Sengoku-period. 
He was the 21st chief of the Chōsokabe clan of Tosa Province (present-day Kōchi Prefecture), the ruler of Shikoku region.

Chōsokabe clan
Chōsokabe clan (Japanese: 長宗我部氏, Hepburn: Chōsokabe-shi), also known as Chōsokame (長宗我部), was a Japanese samurai kin group. Over time, they were known for serving the Hosokawa clan, then the Miyoshi clan and then the Ichijō clan.
2022–23 UEFA Europa Conference League qualifying
2022–23 UEFA Europa Conference League qualifying was the preliminary phase of the 2022–23 UEFA Europa Conference League, prior to the competition proper. Qualification consisted of the qualifying phase (first to third rounds) and the play-off round. It began on 5 July and ended on 25 August 2022.

A total of 166 teams competed in the qualifying system, with 25 teams in Champions Path and 141 teams in Main Path. The 22 winners in the play-off round advanced to the group stage, to join the 10 losers of the Europa League play-off round.

Times are CEST (UTC+2), as listed by UEFA (local times, if different, are in parentheses).

2022–23 UEFA Europa Conference League group stage
The 2022–23 UEFA Europa Conference League group stage began on 8 September 2022 and ended on 3 November 2022. A total of 32 teams competed in the group stage to decide 8 of the 16 places in the knockout phase of the 2022–23 UEFA Europa Conference League.

All teams besides AZ, Basel, CFR Cluj, Gent, Partizan, Slavia Prague and Slovan Bratislava, who competed in last season's group stage, made their debut appearances in the group stage. Ballkani, Djurgårdens IF, Dnipro-1, Pyunik, RFS, Silkeborg, Slovácko, Vaduz and Žalgiris made their debut appearances in a UEFA competition group stage. Ballkani, Vaduz and Žalgiris were the first teams from Kosovo, Liechtenstein and Lithuania, respectively, to play in a UEFA competition group stage.

A total of 28 national associations were represented in the group stage.
Prem Bandhan (1979 film)
Prem Bandhan (transl. The bond of love) is a 1978 Indian Hindi-language romantic drama film directed by Ramanand Sagar. The film stars Rajesh Khanna, Rekha and Moushumi Chatterjee as the lead actors and is supported by A. K. Hangal, Prema Narayan, Bhagwan, Keshto Mukherjee and Lalita Pawar. The film's music is by Laxmikant Pyarelal.

The story revolves around the adventures of Rajesh Khanna after he has amnesia post accident and falls in love with and marries a fisher woman, whereas his sophisticated city-bred girlfriend waits for him in the city. The film had the popular song Main Tere Pyar Mein Pagal sung by Kishore Kumar and Lata Mangeshkar.

Moushumi Chatterjee
Moushumi Chatterjee (born Indira Chattopadhyay; 26 April 1954) is an Indian actress and politician known for her work in Hindi and Bengali cinema. She was one of the highest-paid actresses in Hindi films during the 1970s. She joined the Bharatiya Janata Party in 2019; she was previously a member of the Indian National Congress.
Tim Simpson (American football)
Timothy James Simpson (born March 5, 1969) is an American former professional football player who was an offensive guard for one season with the Pittsburgh Steelers of the National Football League (NFL). He played college football for the Illinois Fighting Illini and was selected by the Cleveland Browns in the twelfth round of the 1992 NFL draft. Simpson was also a member of the New York Jets, London Monarchs, Peoria Pirates and Bloomington Edge.

Illinois Fighting Illini football
The Illinois Fighting Illini football program represents the University of Illinois Urbana-Champaign in college football at the NCAA Division I Football Bowl Subdivision (formerly Division I-A) level. The Fighting Illini are a founding member of the Big Ten Conference, and have played their home games at Gies Memorial Stadium in Champaign, Illinois since 1923. The Fighting Illini are currently led by head coach Bret Bielema.

Illinois claims 15 Big Ten championships, ranking 4th-most among conference members, and 5 national championships, ranking 13th-most among NCAA Division 1 programs.  Illinois has had 27 Consensus All-Americans, and 15 former Illini have been inducted into the College Football Hall of Fame; in the Pro Football Hall of Fame, 6 former Illini have been inducted. Illinois has three trophy rivalries against Northwestern, Purdue, and Ohio State.
Patricia Nyanga Laverley
Patricia Nyanga Laverley is a Sierra Leonean economist and politician. She served as the Deputy Minister of Finance representing Moyamba and Bonthe Districts from 2018–2021. On 12 April 2018, President Julius Maada Bio appointed her as the Deputy Minister of Finance. Before this appointment, she served in various professional and managerial roles at the African Development Bank Group, HSBC, World Bank Group, International Monetary Fund, and Amnesty International.

Ministry of Finance (Sierra Leone)
Sierra Leone Ministry of Finance is a ministerial department of the Government of Sierra Leone, and is in charge of managing the revenue and finances of the Sierra Leone government. The ministry implements the economic policies and is responsible for public financial management. The ministry advises the President of Sierra Leone on economic issues. The headquarters of the Sierra Leone Ministry Of Finance is located on George Street in Freetown, Sierra Leone.

The  Ministry of Finance is headed by the Minister of Finance, who is appointed by the president of Sierra Leone, and must be confirmed by the Parliament of Sierra Leone before taking office. The current Sierra Leone Minister of Finance is Sheku Ahmed Fantamadi Bangura, who was previously Deputy Finance Minister. Since some days his brother has been double rank promoted to CDS in the Sierra Leone army. The President of Sierra Leone has the constitutional authority to fire the Minister of Finance at any time.
Euler–Rodrigues formula
In mathematics and mechanics, the Euler–Rodrigues formula describes the rotation of a vector in three dimensions. It is based on Rodrigues' rotation formula, but uses a different parametrization.

The rotation is described by four Euler parameters due to Leonhard Euler. The Rodrigues' rotation formula  (named after Olinde Rodrigues), a method of calculating the position of a rotated point, is used in some software applications, such as flight simulators and computer games.

Rodrigues' rotation formula
In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation matrix in SO(3), the group of all rotation matrices, from an axis–angle representation. In terms of Lie theory, the Rodrigues' formula provides an algorithm to compute the exponential map from the Lie algebra so(3) to its Lie group SO(3).

This formula is variously credited to Leonhard Euler, Olinde Rodrigues, or a combination of the two. A detailed historical analysis in 1989 concluded that the formula should be attributed to Euler, and recommended calling it "Euler's finite rotation formula." This proposal has received notable support, but some others have viewed the formula as just one of many variations of the Euler–Rodrigues formula, thereby crediting both.