hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Group homomorphism
In mathematics, given two groups, (G,∗) and (H, ·), a group homomorphism from (G,∗) to (H, ·) is a function h : G → H such that for all u and v in G it holds that

where the group operation on the left side of the equation is that of G and on the right side that of H.

From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H,

and it also maps inverses to inverses in the sense that

Hence one can say that h "is compatible with the group structure".

In areas of mathematics where one considers groups endowed with additional structure, a homomorphism sometimes means a map that respects not only the group structure (as above) but also the extra structure. For example, a homomorphism of topological groups is often required to be continuous.

Isomorphism theorems
In mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients, homomorphisms, and subobjects.  Versions of the theorems exist for groups, rings, vector spaces, modules, Lie algebras, and other algebraic structures.  In universal algebra, the isomorphism theorems can be generalized to the context of algebras and congruences.
Fife, Washington
Fife is a city in Pierce County, Washington, United States and a suburb of Tacoma. The population was 10,999 at the 2020 census. Fife is contained within the Puyallup Indian Reservation and bisected by Interstate 5. It is east of Tacoma and the Port of Tacoma.

Auburn, Washington
Auburn is a city in King County, Washington, United States (with a small portion crossing into neighboring Pierce County). The population was 87,256 at the 2020 Census, and was estimated at 85,513 in 2024. Auburn is a suburb in the Seattle metropolitan area, and is currently ranked as the 15th most populous city in the state of Washington.

The Muckleshoot Indian Reservation lies to the south and southeast.
Yellow Breeches Creek
Yellow Breeches Creek, also known as Callapatscink Creek, Callapatschink Creek  (Lenape for "where it returns") or Shawnee Creek is a 56.1-mile-long (90.3 km) tributary of the Susquehanna River in central Pennsylvania, USA. There is no agreed upon explanation for the name Yellow Breeches Creek, which is found in land warrants as early as 1736.

Conodoguinet Creek
Conodoguinet Creek is a 104-mile-long (167 km) tributary of the Susquehanna River in South central Pennsylvania in the United States. The name is Native American, and means "A Long Way with Many Bends".

Conodoguinet Creek joins the Susquehanna River upstream of Harrisburg.

The headwaters for the Conodoguinet lie within the Fort Loudon, PA State Game Lands just East of Cowan's Gap State Park and McConnellsburg, PA. The Creek flows in a northerly direction through several State Games lands before emptying into the LetterKenny Reservoir near Roxbury, PA. From the reservoir, the Creek flows generally East passing Newville, Carlisle, and Mechanicsburg before terminating as it empties into the Susquehanna River.

The water divide between Conodoguinet Creek and Conococheague Creek is sometimes used as the boundary between the Hagerstown Valley and the Cumberland Valley. It flows past many mills, including Maclay's Mill. The Appalachian Trail crosses the creek near Carlisle.
National Collegiate Hockey Conference
The National Collegiate Hockey Conference (NCHC) is an NCAA men's Division I hockey conference. The league was formed on July 9, 2011, and began playing for the 2013–14 season, the same season that the Big Ten Conference began competition, as a combination of six previous members of the WCHA and two of the CCHA. The league is headquartered in Colorado Springs, Colorado.

2024–25 NCHC season
The 2024–25 NCHC season was the 12th season of play for the National Collegiate Hockey Conference and took place during the 2024–25 NCAA Division I men's ice hockey season. The regular season began on October 4, 2024, and concluded on March 8, 2025. The conference tournament began on March 14, 2025 and concluded on March 22, 2025.

This was the first NCHC season for Arizona State.
2019 Asian Men's Volleyball Championship
The 2019 Asian Men's Volleyball Championship  was the twentieth staging of the Asian Men's Volleyball Championship, a biennial international volleyball tournament organised by the Asian Volleyball Confederation (AVC) with Islamic Republic of Iran Volleyball Federation (IRIVF). The tournament was held in Tehran, Iran from 13 to 21 September 2019.

Top eight teams which had not yet qualified to the 2020 Summer Olympics qualified for the 2020 Asian Olympic Qualification Tournament.

2021 Asian Men's Volleyball Championship
The 2021 Asian Men's Volleyball Championship was the twenty-first staging of the Asian Men's Volleyball Championship, a biennial international volleyball tournament organised by the Asian Volleyball Confederation (AVC) with Japan Volleyball Association (JVA). The tournament was held in Chiba and Funabashi, Japan from 12 to 19 September 2021.

The top two teams of the tournament qualified for the 2022 FIVB Volleyball Men's World Championship as the AVC representatives.
Project A Part II
Project A Part II (Chinese: A計劃續集; aka Jackie Chan's Project A II; released in the Philippines as Super Fighter) is a 1987 Hong Kong action film starring and directed by Jackie Chan. It co-stars Maggie Cheung, Bill Tung, and Rosamund Kwan. It is the sequel to the 1983 film Project A. Chan plays Sergeant Dragon Ma once again, but his co-stars from the previous film, Sammo Hung and Yuen Biao, are both absent. The film was released theatrically in Hong Kong on 19 August 1987.

Miracles (1989 film)
Miracles (Chinese: 奇蹟; pinyin: qí jī; Jyutping: kei zik; released under various titles for several territories worldwide) is a 1989 Hong Kong crime action comedy film starring and directed by Jackie Chan, and written by Chan and Edward Tang. It is set in 1930s Hong Kong and is an adaptation of Frank Capra's Lady for a Day (1933) and Pocketful of Miracles (1961), which in turn were based on "Madame La Gimp", a 1929 short story by Damon Runyon.

Miracles features many well-known Hong Kong actors, including Anita Mui and Wu Ma, and is considered one of Jackie Chan's most sophisticated directorial efforts. Chan is an ardent fan of Hollywood musicals, and Miracles pays a tribute to that genre. According to his autobiography, Chan stated that this was one of his favorite films he has made. The film was remade in Hindi as Singh Is Kinng with Akshay Kumar and Katrina Kaif.
Provinces of Turkey
Turkey is divided into 81 provinces (Turkish: il). Each province is divided into a number of districts (ilçe). Each provincial government is seated in the central district (merkez ilçe). For non-metropolitan municipality designated provinces, the central district bears the name of the province (e.g. the city/district of Rize is the central district of Rize Province). In the Ottoman Empire, the corresponding unit was the vilayet.

Each province is administered by an appointed governor (vali) from the Ministry of the Interior.

İzmir Province
İzmir Province (Turkish: İzmir ili) is a province and metropolitan municipality of Turkey in western Anatolia, situated along the Aegean coast. Its capital is the city of İzmir, which is in itself composed of the province's central 11 districts out of 30 in total. To the west, it is surrounded by the Aegean Sea, and it encloses the Gulf of Izmir. Its area is 11,891 square kilometres (4,591 square miles), and its population is 4,462,056 (2022). Neighboring provinces are Balıkesir to the north, Manisa to the east, and Aydın to the south. The traffic code of the province is 35.

Major rivers of the province include the Küçük Menderes river, Koca Çay (with Güzelhisar dam), and Bakırçay.
Amphicyonidae
Amphicyonidae is an extinct family of terrestrial carnivorans belonging to the suborder Caniformia. They first appeared in North America in the middle Eocene (around 45 Ma), spread to Europe by the late Eocene (35 Ma), and further spread to Asia and Africa by the early Miocene (23 Ma). They had largely disappeared worldwide by the late Miocene (9-7 Ma), with the latest recorded species at the end of the Miocene in Africa. They were among the first carnivorans to evolve large body size. Amphicyonids are colloquially referred to as "bear-dogs".

Chalicotheriidae
Chalicotheriidae (from Ancient Greek χάλιξ (khálix), meaning "gravel", and θηρίον (theríon), meaning "beast") is an extinct family of herbivorous, perissodactyl mammals that lived in North America, Eurasia, and Africa from the Middle Eocene to the Early Pleistocene. They are often called chalicotheres, a term which is also applied to the broader grouping of Chalicotherioidea. They are noted for their unusual morphology compared to other ungulates, such as their clawed forelimbs. Members of the subfamily Chalicotheriinae developed elongated gorilla-like forelimbs that are thought to have been used to grasp vegetation. They are thought to have been browsers on foliage as well as possibly bark and fruit.
Vladimir Ashkenazy
Vladimir Davidovich Ashkenazy (Russian: Влади́мир Дави́дович Ашкена́зи, tr. Vladimir Davidovich Ashkenazi; born 6 July 1937) is a Soviet-born Icelandic pianist, chamber music performer, and conductor. Ashkenazy has collaborated with well-known orchestras and soloists. In addition, he has recorded a large repertoire of classical and romantic works. His recordings have earned him seven Grammy Awards and he has been awarded three stages of Iceland's Order of the Falcon for his overall contribution to music.

Van Cliburn
Harvey Lavan "Van" Cliburn Jr. (July 12, 1934 – February 27, 2013) was an American pianist. At the age of 23, Cliburn achieved worldwide recognition when in 1958 he won the inaugural International Tchaikovsky Competition in Moscow.

Cliburn's mother, a piano teacher and an accomplished pianist in her own right, discovered him playing at age three, mimicking one of her students, and arranged for him to start taking lessons. Cliburn developed a rich, round tone and a singing-voice-like phrasing, having been taught from the start to sing each piece. Cliburn toured domestically and overseas. He played for royalty, heads of state, and every US president from Harry S. Truman to Barack Obama.
Greg Chappell
Gregory Stephen Chappell AO MBE (born 7 August 1948) is a former cricketer who represented Australia at international level in both Tests and One-Day Internationals (ODI). The second of three brothers to play Test cricket, Chappell was the pre-eminent Australian batsman of his time who allied elegant stroke making to fierce concentration. An exceptional all round player who bowled medium pace and, at his retirement, held the world record for the most catches in Test cricket, Chappell's career straddled two eras as the game moved toward a greater level of professionalism after the WSC schism. He was the vice captain of the Australian squad which finished as runners-up at the 1975 Cricket World Cup.

Since his retirement as a player in 1984, Chappell has pursued various business and media interests as well as maintaining connections to professional cricket; he has been a selector for national and Queensland teams, a member of the Australian Cricket Board, and a coach.

Gary Cosier
Gary John Cosier (born 25 April 1953) is a former Australian international cricketer who played in 18 Test matches and nine One Day Internationals between 1975 and 1979. Cosier's star shone very briefly following a sensational debut, when he became only the ninth Australian to post a century in his first Test.
Trey Lorenz
Trey Lorenz (born Lloyd Lorenz Smith; January 19, 1969) is an American R&B singer-songwriter and record producer. He was born in Florence, South Carolina and is a graduate of Wilson High School. Lorenz is best known for his duet with recording artist Mariah Carey on "I'll Be There", a cover of the 1970 number-one Jackson 5 recording of the same name. The record topped the US Billboard Hot 100 and R&B singles chart a second time in 1992 and earned Lorenz and Carey both a Grammy Award nomination for Best R&B Performance by a Duo or Group with Vocals. They would later perform the song again at the funeral of Michael Jackson on July 7, 2009. He is also known for his 1992 hit single "Someone to Hold".

The Adventures of Mimi
The Adventures of Mimi was a 2006 concert tour of arenas by American singer-songwriter Mariah Carey. It was the sixth concert tour of her then-sixteen-year career, and was named after a fan's “Carey-centric” diary of the same name, in addition to her album at the time, The Emancipation of Mimi. The bus tour started in late July and ended in October, with two stops in Tunisia, twenty-five stops in the United States, seven in Canada and six in Japan.
Samson and Delilah (opera)
Samson and Delilah (French: Samson et Dalila), Op. 47, is a grand opera in three acts and four scenes by Camille Saint-Saëns to a French libretto by Ferdinand Lemaire. It was first performed in Weimar at the Grossherzogliches (Grand Ducal) Theater (now the Staatskapelle Weimar) on 2 December 1877 in a German translation.

The opera is based on the Biblical tale of Samson and Delilah found in Chapter 16 of the Book of Judges in the Old Testament. It is the only opera by Saint-Saëns that is regularly performed. The second act love scene in Delilah's tent is one of the set pieces that define French opera. Two of Delilah's arias are particularly well known: "Printemps qui commence" ("Spring begins") and "Mon cœur s'ouvre à ta voix" ("My heart opens itself to your voice", also known as "Softly awakes my heart"), the latter of which is one of the most popular recital pieces in the mezzo-soprano/contralto repertoire.

William Tell (opera)
William Tell (French: Guillaume Tell; Italian: Guglielmo Tell) is a French-language opera in four acts by Italian composer Gioachino Rossini to a libretto by Victor-Joseph Étienne de Jouy and L. F. Bis, based on Friedrich Schiller's play Wilhelm Tell, which, in turn, drew on the William Tell legend. The opera was Rossini's last, although he lived for nearly 40 more years. Fabio Luisi said that Rossini planned for Guillaume Tell to be his last opera even as he composed it. The often-performed overture in four sections features a depiction of a storm and a vivacious finale, the "March of the Swiss Soldiers".

Paris Opéra archivist Charles Malherbe discovered the original orchestral score of the opera in the hands of a second-hand bookseller, resulting in its being acquired by the Paris Conservatoire in 1898.
Johnny Walker (actor)
Badruddin Jamaluddin Kazi (1924? – 29 July 2003), professionally known as Johnny Walker, was an Indian actor and comedian who acted in around 300 films. He was best known for his humorous roles in Indian films, notably being typecast as a hapless drunkard.

Shyama (Hindi actress)
Shyama (born Khurshid Akhtar; 7 June 1935 – 14 November 2017) was an Indian actress who appeared in Hindi and Punjabi films. She first appeared as a child artist in the 1945 Hindi film Zeenat as Baby Khurshid. She later adopted the screen name Shyama, given to her by film director Vijay Bhatt. After years of playing small parts and side roles in films like Shabnam (1949) and Tarana (1951), her breakthrough in a starring adult role came with Aar Paar (1954). She also had some success in Punjabi films like Posti (1950) and Kaude Shah (1953).

Known for her versatility in various genres, Shyama went on to become a recognized star in both Hindi and Punjabi cinema in the 1950s and early 1960s. Some of her best known roles were in Sharada (1957), Bhabhi (1957), Barsaat Ki Raat (1960) and Zabak (1961). She later transitioned to taking on character roles in films like Milan (1967), Sawan Bhadon (1970) and her last film Hathyar (1989), after which she retired from acting.
STS-85
STS-85 was the 23rd flight of Space Shuttle Discovery that performed multiple space science packages. It was launched from Kennedy Space Center, Florida, on 7 August 1997. The main STS-85 payloads included the satellite known as Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere-Shuttle Pallet Satellite-2 CRISTA-SPAS-02.

Kent Rominger
Kent Vernon "Rommel" Rominger (born August 7, 1956) is an American former astronaut, former NASA Chief of the Astronaut Office at Johnson Space Center, and a captain in the United States Navy. Rominger holds the Space Shuttle Orbiter flight time record with 1610 hours. He joined ATK Launch Systems Group in 2006 as Vice President of Advanced Programs.
Radio Nacional (Spanish radio station)
Radio Nacional is a Spanish free-to-air radio station owned and operated by Radio Nacional de España (RNE), the radio division of state-owned public broadcaster Radiotelevisión Española (RTVE). It is the corporation's flagship radio station, and is known for broadcasting mainstream and generalist programming, including news bulletins, current affairs, sports and entertainment.

It was launched on 19 January 1937 as Franco's official radio under the department of propaganda during the Spanish Civil War. The station was initially simply referred to as "Radio Nacional de España". It received other names, such as "RNE 1" from 1988 until 1999 and "Radio 1" from 1999 until 2008 when it adopted its current name "Radio Nacional".

Ràdio 4
Ràdio 4 is a Spanish free-to-air radio station owned and operated by Radio Nacional de España (RNE), the radio division of state-owned public broadcaster Radiotelevisión Española (RTVE). It is the corporation's Catalan language radio station, and is available in Catalonia and Andorra. It was launched on 13 December 1976.
Midland Railway
The Midland Railway (MR) was a railway company in the United Kingdom from 1844. The Midland was one of the largest railway companies in Britain in the early 20th century, and the largest employer in Derby, where it had its headquarters. It amalgamated with several other railways to create the London, Midland and Scottish Railway at grouping in 1923.

The Midland had a large network of lines emanating from Derby, stretching to London St Pancras, Manchester, Carlisle, Birmingham, and Bristol. It expanded as much through acquisitions as by building its own lines. It also operated ships from Heysham in Lancashire to Douglas and Belfast. A large amount of the Midland's infrastructure remains in use and visible, such as the Midland Main Line and the Settle–Carlisle line, and some of its railway hotels still bear the name Midland Hotel.

Nickey line
The Nickey line (also known as the Harpenden to Hemel Hempstead branch railway) is a disused railway that once linked the towns of Hemel Hempstead and Harpenden (initially Luton), via Redbourn, in Hertfordshire, England. The former trackbed has been redeveloped as a rail trail and is part of the Oxford to Welwyn Garden City route of the National Cycle Network. It is approximately 9 miles (14 km) long.
Bappi Lahiri
Bappi Aparesh Lahiri (born Alokesh Aparesh Lahiri; 27 November 1952 – 15 February 2022), also known as Bappi Da, was an Indian singer, composer and record producer. He popularised the use of synthesised disco music in Indian music industry and sang some of his own compositions.  He was popular in the 1980s and 1990s with filmi soundtracks.  He delivered major box office successes primarily in Hindi, Telugu, and Bengali films. His music was well received into the 21st century.

In 1986, he was recognised by Guinness World Records for recording more than 180 songs in one year.

Viju Shah
Vijay Shah (born 5 June 1959), popularly known as Viju Shah, is an Indian composer in the Hindi film industry. He is the son of Kalyanji Virji Shah, one-half of the composer duo Kalyanji–Anandji.

Shah has composed soundtracks for over 20 Hindi films, including Tridev (1989), Vishwatma (1992), Mohra (1994), Gupt: The Hidden Truth (1997), and Bade Miyan Chote Miyan (1998). He won the Filmfare Award for Best Background Score in 1998 for his work in Gupt: The Hidden Truth.
Owen Nolan
Owen Liam Nolan (born 12 February 1972) is a Canadian former professional ice hockey player. He was drafted first overall by the Quebec Nordiques in the 1990 NHL entry draft. During his 18-year NHL career, he played for the Nordiques, Colorado Avalanche, San Jose Sharks, Toronto Maple Leafs, Phoenix Coyotes, Calgary Flames, Minnesota Wild, as well as playing a season with the ZSC Lions of National League A. Born in Belfast, he was raised in Thorold, Ontario and played for Canada internationally. A five-time NHL All-Star, Nolan is widely known as a power forward.

Mike Ricci (ice hockey)
Michael Ricci (born October 27, 1971) is a Canadian former professional ice hockey centre who played 16 seasons in the National Hockey League (NHL) for the Philadelphia Flyers, Quebec Nordiques, Colorado Avalanche, San Jose Sharks and Phoenix Coyotes.

Ricci currently serves in the Sharks front office as a scout & development coach.
Victoria Eugenie of Battenberg
Victoria Eugenie Julia Ena of Battenberg (24 October 1887 – 15 April 1969), commonly known as Ena, was Queen of Spain as the wife of King Alfonso XIII from their marriage on 31 May 1906 until 14 April 1931, when the Second Spanish Republic was proclaimed.

A princess of the Grand Duchy of Hesse by birth, she was a member of the Battenberg family, a morganatic branch of the House of Hesse-Darmstadt. She was the youngest granddaughter of Queen Victoria and Prince Albert of Saxe-Coburg and Gotha.

Unlike most members of the Battenberg family, who bore the style of Serene Highness, Victoria Eugenie was born with the style of Highness, by virtue of a royal warrant issued by Queen Victoria in 1886. Prior to her marriage, she was elevated to the style of Royal Highness by her uncle, King Edward VII.

Prince Maurice of Battenberg
Prince Maurice of Battenberg (Maurice Victor Donald; 3 October 1891 – 27 October 1914) was a member of the Hessian princely Battenberg family and the extended British royal family, and the youngest grandchild of Queen Victoria. He was styled as Prince Maurice throughout his life and died before the Battenberg family anglicised their surname to Mountbatten in 1917, meaning he was never known by that name.
2018 Masters Tournament
The 2018 Masters Tournament was the 82nd edition of the Masters Tournament and the first of golf's four major championships in 2018. It was held April 5–8 at Augusta National Golf Club in Augusta, Georgia.

Patrick Reed won his first major title with a final round 71 (−1) for 273 (−15), one stroke ahead of runner-up Rickie Fowler.

2018 U.S. Open (golf)
The  2018 United States Open Championship was the 118th U.S. Open, held June 14–17 at Shinnecock Hills Golf Club in Shinnecock Hills, New York, about eighty miles (130 km) east of New York City on Long Island; it was the fifth time the U.S. Open was held at this course.

Defending champion Brooks Koepka shot a final round 68 for 281 (+1) to win his second straight U.S. Open, one stroke ahead of runner-up Tommy Fleetwood, who closed with the sixth round of 63 in U.S. Open history. Koepka was only the third to successfully defend the title since World War II, following Ben Hogan (1951) and Curtis Strange (1989).

The USGA changed the playoff format in February, from a full round (18 holes) to a two-hole aggregate playoff. Previously, playoffs at the U.S. Open were 18 holes, followed by sudden-death, if needed. The last 18-hole playoff was in 2008, won by Tiger Woods on the first sudden-death hole.
Poul Anderson
Poul William Anderson (/ˈpoʊəl/ POH-əl; November 25, 1926 – July 31, 2001) was an American fantasy and science fiction author who was active from the 1940s until his death in 2001. Anderson also wrote historical novels. He won the Hugo Award seven times and the Nebula Award three times, and was nominated many more times for awards.

David Brin
Glen David Brin (born October 6, 1950) is an American science fiction author. He has won the Hugo, Locus, Campbell and Nebula Awards. His novel The Postman was adapted into a 1997 feature film starring Kevin Costner.