hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
No small subgroup
In mathematics, especially in topology, a topological group  is said to have no small subgroup if there exists a neighborhood  of the identity that contains no nontrivial subgroup of  An abbreviation '"NSS"' is sometimes used. A basic example of a topological group with no small subgroup is the general linear group over the complex numbers.

A locally compact, separable metric, locally connected group with no small subgroup is a Lie group. (cf. Hilbert's fifth problem.)

Hilbert's fifth problem
Hilbert's fifth problem is the fifth mathematical problem from the problem list publicized in 1900 by mathematician David Hilbert, and concerns the characterization of Lie groups.

The theory of Lie groups describes continuous symmetry in mathematics; its importance there and in theoretical physics (for example quark theory) grew steadily in the twentieth century. In rough terms, Lie group theory is the common ground of group theory and the theory of topological manifolds. The question Hilbert asked was an acute one of making this precise: is there any difference if a restriction to smooth manifolds is imposed?

The expected answer was in the negative (the classical groups, the most central examples in Lie group theory, are smooth manifolds). This was eventually confirmed in the early 1950s. Since the precise notion of "manifold" was not available to Hilbert, there is room for some debate about the formulation of the problem in contemporary mathematical language.
Odd–even sort
In computing, an odd–even sort or odd–even transposition sort (also known as brick sort or parity sort) is a relatively simple sorting algorithm, developed originally for use on parallel processors with local interconnections.  It is a comparison sort related to bubble sort, with which it shares many characteristics.  It functions by comparing all odd/even indexed pairs of adjacent elements in the list and swapping pairs where in the wrong order (where the first is larger than the second). The next step repeats this for even/odd indexed pairs (of adjacent elements). Then it alternates between odd/even and even/odd steps until the list is sorted.

Bubble sort
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps have to be performed during a pass, meaning that the list has become fully sorted. The algorithm, which is a comparison sort, is named for the way the larger elements "bubble" up to the top of the list.

It performs poorly in real-world use and is used primarily as an educational tool. More efficient algorithms such as quicksort, timsort, or merge sort are used by the sorting libraries built into popular programming languages such as Python and Java.
Mondo film
Mondo film is a subgenre of exploitative documentary films. Many mondo films are pseudo-documentaries and usually depict sensational topics, scenes, or situations. Common traits of mondo films include portrayals of foreign cultures (which have drawn accusations of ethnocentrism or racism), an emphasis on taboo subjects such as death and sex, and staged sequences presented as genuine documentary footage. Over time, the films have placed increasing emphasis on footage of the dead and dying (both real and fake).

The term mondo is Italian for 'world'. The term shockumentary is also used to describe the genre.

Mondo films began to soar in popularity in the 1960s with the releases of Mondo Cane (1962), Women of the World (1963) and Africa Addio (1966). The genre arguably reached its peak with Faces of Death (1978), a film that inspired myriad imitators, such as Banned from Television, Death Scenes, and the Traces of Death  and Faces of Gore series.

Pseudo-documentary
A pseudo-documentary or fake documentary is a film or video production that takes the form or style of a documentary film but does not portray real events. Rather, scripted and fictional elements are used to tell the story. The pseudo-documentary, unlike the related mockumentary, is not always intended as satire or humor. It may use documentary camera techniques but with fabricated sets, actors, or situations, and it may use digital effects to alter the filmed scene or even create a wholly synthetic scene.
Melanocetus murrayi
Melanocetus murrayi, commonly known as Murray's abyssal anglerfish, is a deep sea anglerfish in the family Melanocetidae, found in tropical to temperate parts of the world's oceans at depths down to over 2,000 m (6,600 ft).

Black seadevil
Black seadevils are small, deep-sea lophiiform fish of the family Melanocetidae. The six known species are all within the genus Melanocetus. They are found in tropical to temperate waters of the Atlantic, Indian, and in the Pacific Oceans, as well as one other species endemic to the Ross Sea.

One of several anglerfish families, black seadevils are named for their intimidating appearance and dark skin. The humpback anglerfish (Melanocetus johnsonii) was featured on a 1995 cover of Time magazine and became a flagship species for deep sea fauna.
Stroud and District Combination Senior Cup
The Stroud and District Combination Senior Cup is an annual rugby union knock-out club competition organized by the Stroud and District Combination - one of the five bodies that make up the Gloucestershire Rugby Football Union.  It was first introduced during the 1974-75 season, with the inaugural winners being the Royal Agricultural College and is the most important rugby union competition in Stroud District, ahead of the Junior Cup and Bill Adams Cup.  With only 9 member clubs the combination is one of the smallest in Gloucestershire.

The Senior Cup is currently open to club sides based in Stroud District which can range between tier 7 (Tribute Western Counties North) all the way down to tier 11 (Gloucester 3).  
The format is a knockout cup with semi-finals followed by a final to be held at a neutral ground in the region between March-May.

Stroud and District Combination Bill Adams Cup
The Stroud and District Combination Bill Adams Cup is an annual rugby union knock-out club competition organised by the Stroud and District Combination – one of the five bodies that make up the Gloucestershire Rugby Football Union.  It was first introduced during the 1983–84 season, with the first ever winners being Cirencester III.  The Bill Adams Cup is the third most important cup competition in Stroud District behind the Senior Cup (1st) and Stroud and District Combination Junior Cup (2nd).  With only 9 member clubs the combination is one of the smallest in Gloucestershire.

The Bill Adams Cup is currently open to the 2nd and 3rd teams of clubs location within the Stroud District.  The format is a knock-out cup with semi-finals and a final, with the final to be held a neutral ground between March–May.
Honda CBR1000RR
The Honda CBR1000RR, marketed in some countries with the Fireblade suffix (capitalized as FireBlade until the 2000s), is a sport bike produced by Honda since 2004 as the seventh generation of the CBR Fireblade series of motorcycles that began with the CBR900RR in 1992.

Honda CBR900RR
The Honda CBR900RR, or Fireblade in some countries, is a  900 cc (55 cu in) sport bike, part of the CBR series introduced in 1992 by Honda.  It was the first of a series of large-displacement Honda models to carry the RR suffix.  The development of the first generation CBR900RR was led by Tadao Baba.
Harry Solomon
Harry S. Solomon is a character in 3rd Rock from the Sun, played by French Stewart. He is the brother of Dick Solomon and Sally Solomon, and the uncle of Tommy Solomon. His middle initial is mentioned in the episode "Dick the Vote." French Stewart said in a 1998 interview, "The way the character was originally described to me was he would be an idiot on any planet. So he's got to be the biggest idiot in the universe!"

Dick Solomon
Dr. Dick Solomon is a character played by John Lithgow in the late-1990s NBC sitcom 3rd Rock from the Sun.  Solomon is the High Commander of a highly trained alien unit, sent to Earth by their leader, The Big Giant Head. His crew is made up of Sally Solomon (played by Kristen Johnston), Harry Solomon (played by French Stewart), and Tommy Solomon (played by Joseph Gordon-Levitt). In the first episode, "Brains and Eggs", Dick states that he has made a home of a "third rate planet, has a job at a third rate university, and now we are looking at a third floor apartment."
2011–12 Scottish Third Division
The 2011–12 Scottish Football League Third Division (also known as the 2011–12 Irn Bru Scottish Football League Third Division for sponsorship reasons) was the 18th season in the current format of 10 teams in the fourth-tier of Scottish football. The season started on 6 August 2011 and finished on 5 May 2012.

Alloa Athletic secured the Third Division title on 7 April 2012, ending their one-year spell in the bottom tier of the Scottish Football League. A second promotion place is available through the play-offs which will be contested by runners-up Queen's Park along with Stranraer, Elgin City, and Albion Rovers of the Second Division. There is no relegation from this division but East Stirlingshire finished bottom for the sixth time in 10 years.

2011–12 Scottish Second Division
The 2011–12 Scottish Football League Second Division (also known as the 2011–12 Irn Bru Scottish Football League Second Division for sponsorship reasons) is the 18th season in the current format of 10 teams in the third-tier of Scottish football. Livingston F.C. are the current champions.
Taxation in Australia
Income taxes are the most significant form of taxation in Australia, and collected by the federal government through the Australian Taxation Office (ATO). Australian GST revenue is collected by the Federal government, and then paid to the states under a distribution formula determined by the Commonwealth Grants Commission.

Australians pay tax for the provision of healthcare, education, defense, roads and railways and for payments to welfare, disaster relief and pensions.

Goods and services tax (Australia)
Goods and Services Tax (GST) in Australia is a value added tax of 10% on most goods and services sales, with some exemptions (such as for certain food, healthcare and housing items) and concessions (including qualifying long-term accommodation, which is taxed at an effective rate of 5.5%). GST is levied on most transactions in the production process, but is in many cases refunded to all parties in the chain of production other than the final consumer.

The tax was introduced by the Howard government and commenced on 1 July 2000, replacing the previous federal wholesale sales tax system and designed to phase out a number of various State and Territory Government taxes, duties and levies such as banking taxes and stamp duty.

A proposed increase of GST to 15% has been put forward, but is generally lacking in bipartisan support.
Captured Hehalutz fighters photograph
A well-known Holocaust photograph depicts three Jewish women who fought in the Warsaw Ghetto Uprising, took shelter in a bunker with a weapons cache, and were forced out by SS soldiers. One of the women, Bluma Wyszogrodzka (center), was shot. The other two, Małka Zdrojewicz (right) and Rachela Wyszogrodzka (left) were marched to the Umschlagplatz and deported to Majdanek concentration camp, where Wyszogrodzka was murdered.

Jürgen Stroop, the SS officer who commanded the suppression of the uprising, admired the bravery of female combatants and included the photograph in one of the copies of his official report. The photograph has become symbolic of Jewish resistance to the Holocaust.

Stroop Report
The Stroop Report is an official report prepared by General Jürgen Stroop for the SS chief Heinrich Himmler, recounting the German suppression of the Warsaw Ghetto Uprising and the liquidation of the ghetto in the spring of 1943. Originally titled The Jewish Quarter of Warsaw Is No More! (Ger. Es gibt keinen jüdischen Wohnbezirk in Warschau mehr!), it was published in the 1960s.
Kovan, Singapore
Kovan (IPA: /ˈkoʊvən/ KOH-vən; Chinese: 高文; pinyin: Gāo Wén) is a neighbourhood located within the town of Hougang, in Singapore. The neighbourhood today largely consists of private housing properties, where majority of the residents live in terrace homes, semi-detached houses and bungalows.

Hougang
Hougang (locally /ˌ(h)aʊˈkɑːŋ, -ʌŋ/ (h)ow-KUNG), archaically spelt Aukang, is a planning area and mature residential town located in the North-East Region of Singapore. It is the largest housing estate in Singapore based on land area, and is home to 247,528 residents as of 2018. Hougang planning area is bordered by Sengkang to the north, Geylang to the south, Bedok to the southeast, Toa Payoh to the southwest, Serangoon to the west and Paya Lebar to the east.
Coalbrookdale Museum of Iron
The Coalbrookdale Museum of Iron is one of ten Ironbridge Gorge Museums administered by the Ironbridge Gorge Museum Trust. The museum is based in the town of Coalbrookdale in the Ironbridge Gorge, in Shropshire, England, within a World Heritage Site, the birthplace of the Industrial Revolution.

Ironbridge Gorge Museum Trust
52°38′20″N 2°29′35″W﻿ / ﻿52.639°N 2.493°W﻿ / 52.639; -2.493

The Ironbridge Gorge Museum Trust is an industrial heritage organisation which runs ten museums and manages multiple historic sites within the Ironbridge Gorge World Heritage Site in Shropshire, England, widely considered as the birthplace of the Industrial Revolution.

The Gorge includes a number of settlements important to industrial history and with heritage assets, including Ironbridge, Coalport and Jackfield along the River Severn, and also Coalbrookdale and Broseley. The area was among the first sites in the United Kingdom to be declared a World Heritage Site by UNESCO in 1986. In 1977, the Ironbridge Gorge Museum was awarded National Heritage Museum of the Year. In 2025 plans were put in place for the National Trust to take over the various museums on 2 March 2026.  A total cost for the transfer has not been announced but is aided by a £9 million grant from the Department for Culture Media and Sport.
Galician People's Union
The Galician People's Union (Galician: Unión do Povo Galego) is a Galician nationalist and communist political party, and is one of the registered political parties of Spain. The party publishes the magazine Terra e Tempo, and the secretary general is Néstor Rego.

It was founded in 1964 with the intention of the independence of Galicia and its transformation into a socialist state. It caused the creation of nationalist fronts such as the Galician National-Popular Assembly and the Bloque Nacionalista Galego. Since 1982 it is one of the parties in the coalition. The current National Spokesperson (Ana Pontón) of the BNG is a member of the UPG.

Galician National-Popular Assembly
The Galician National-Popular Assembly (AN-PG, Asemblea Nacional-Popular Galega in Galician language) was suprapartisan umbrella organization established in 1975 created to coordinate various political fronts of the left-wing Galician nationalist movement.
Kazachinsky District
Kazachinsky District (Russian: Каза́чинский райо́н) is an administrative and municipal district (raion), one of the forty-three in Krasnoyarsk Krai, Russia. It is located in the southern central part of the krai and borders with Yeniseysky and Motyginsky Districts in the north, Taseyevsky District in the east, Bolshemurtinsky District in the south, and with Pirovsky District in the west. The area of the district is 5,755 square kilometers (2,222 sq mi). Its administrative center is the rural locality (a selo) of Kazachinskoye. Population:  11,430 (2010 Census); 12,732 (2002 Census); 16,015 (1989 Soviet census). The population of Kazachinskoye accounts for 33.8% of the district's total population.

Taseyevsky District
Taseyevsky District (Russian: Тасе́евский  райо́н) is an administrative and municipal district (raion), one of the forty-three in Krasnoyarsk Krai, Russia. It is located in the south of the krai and borders with Motyginsky and Boguchansky Districts in the north, Abansky District in the east, Dzerzhinsky District in the southeast, Sukhobuzimsky District in the south, and with Bolshemurtinsky and Kazachinsky Districts in the west. The area of the district is 9,923 square kilometers (3,831 sq mi). Its administrative center is the rural locality (a selo) of Taseyevo. Population:  13,255 (2010 Census); 15,275 (2002 Census); 18,707 (1989 Soviet census). The population of Taseyevo accounts for 60.6% of the district's total population.
Blackwood Farm
Blackwood Farm is a 2002 vampire novel by American writer Anne Rice, the ninth book in her The Vampire Chronicles series. The novel includes some characters who cross over from Rice's Lives of the Mayfair Witches trilogy (1990–1994), continuing the unified story begun in Merrick (2000).

Lives of the Mayfair Witches
Lives of the Mayfair Witches is a trilogy of Gothic supernatural horror fantasy novels by American author Anne Rice. It centers on a family of witches whose fortunes have been guided for generations by a spirit named Lasher. The series began in 1990 with The Witching Hour, which was followed by the sequels Lasher (1993) and Taltos (1994). All three novels debuted at No. 2 on The New York Times Best Seller list.

Some characters from the trilogy cross over to Rice's The Vampire Chronicles, a series of gothic horror novels featuring the vampire Lestat de Lioncourt, specifically in Merrick (2000), Blackwood Farm (2002), and Blood Canticle (2003).

A television series adaptation, Mayfair Witches, debuted on AMC in 2023.
Leone Ginzburg
Leone Ginzburg (Italian: [leˈoːne ˈɡintsburɡ, - ˈɡin(d)zburɡ], Russian: [ˈɡʲinzbʊrk]; 4 April 1909 – 5 February 1944) was an Italian editor, writer, journalist and teacher, as well as an important anti-fascist political activist and a hero of the resistance movement. He was the husband of the renowned author Natalia Ginzburg and the father of the historian Carlo Ginzburg.

Natalia Ginzburg
Natalia Levi Ginzburg (Italian: [nataˈliːa ˈlɛːvi ˈɡintsburɡ, - ˈɡin(d)zburɡ]; later Levi Baldini; née Levi; 14 July 1916 – 7 October 1991) was an Italian author whose work explored family relationships, politics during and after the Fascist years and World War II, and philosophy. She wrote novels, short stories and essays, for which she received the Strega Prize and Bagutta Prize.  Most of her works were also translated into English and published in the United Kingdom and the United States.

An activist, for a time in the 1930s she belonged to the Italian Communist Party. In 1983, she was elected to Parliament from Rome as an independent politician.
Andy Irons
Philip Andrew Irons (July 24, 1978 – November 2, 2010) was an American professional surfer. He began surfing with his brother Bruce on the shallow and dangerous waves of Kauai, Hawaii, before being spotted by a local surfboard brand and flown to North Shore, Oahu, Hawaii, to compete and develop his skill.

Over the course of his professional career, Irons won three world titles (2002, 2003, 2004), three Quiksilver Pro France titles (2003, 2004, 2005), two Rip Curl Pro Search titles (2006 and 2007), and 20 elite-tour victories, including the Vans Triple Crown of Surfing four times from 2002 to 2006. He won at nearly every venue on the ASP calendar, only missing Gold Coast, Brazil, and Portugal.

Bruce Irons (surfer)
Bruce Irons (born November 16, 1979) is an American regularfoot professional surfer from Hanalei, Kauai, and is often regarded as one of the best tuberiders of all time. He is the younger brother of three-time world champion Andy Irons.
Enrique Ika
Enrique Ika a Tuʻu Hati (c. 1859 – after 1900) was elected ‘ariki (king) of Rapa Nui (Easter Island) in 1900 and led a failed rebellion. He was one of the last Rapa Nui to claim the traditional kingship in the early 20th-century. However, he is not remembered as the last king; instead his predecessor Riro Kāinga is generally regarded as the last king, although neither held much power.

Riro Kāinga
Siméon or Timeone Riro ʻa Kāinga Rokoroko He Tau (died 1898 or 1899) was the last ‘ariki (king) of Rapa Nui (Easter Island) from 1892 until his death. He ruled the island during a brief period of indigenous autonomy between Chile's initial annexation in 1888 and the country's reassertion of colonial authority in 1896. Riro died unexpectedly during a diplomatic trip to Chile to discuss the island's sovereignty with colonial authorities, leading to suspicions that he had been poisoned.
Battle of Sourton Down
The Battle of Sourton Down took place on 25 April 1643, near Sourton, in Devon, during the First English Civil War. A Parliamentarian force under James Chudleigh defeated a Royalist army under Sir Ralph Hopton. Casualties on both sides were light, and the result had little impact on the strategic position in the West Country.

Hoping to surprise their opponents, the Royalist army undertook a night march on the Parliamentarian base in Okehampton. However, they in turn were ambushed by a small force of cavalry led by Chudleigh, and routed.
Hopton was forced to abandon most of his baggage and supplies, but won a decisive battle at Stratton three weeks later.

Battle of Stratton
The Battle of Stratton, also known as the Battle of Stamford Hill, took place on 16 May 1643, at Stratton in Cornwall, during the First English Civil War. In the battle, the Royalists destroyed the Parliamentarians' field army in Devon and Cornwall.
Mount Unzen
Mount Unzen (雲仙岳, Unzen-dake) is an active volcanic group of several overlapping stratovolcanoes, near the city of Shimabara, Nagasaki on the island of Kyushu, Japan's southernmost main island.

In 1792, the collapse of one of its several lava domes triggered a megatsunami that killed 14,524 people in Japan's worst volcanic-related disaster. The volcano was most recently active from 1990 to 1995, and a large eruption in 1991 generated a pyroclastic flow that killed 43 people, including three volcanologists.

Its highest peaks are Fugen-dake (普賢岳) at 1,359 metres (4,459 ft) and Heisei-shinzan (平成新山) at 1,486 metres (4,875 ft). The latter emerged during the eruptions of the early, eponymous Heisei era (1989–2019).

1792 Unzen landslide and tsunami
The 1792 Unzen landslide and tsunami resulted from the volcanic activities of Mount Unzen (in the Shimabara Peninsula of Nagasaki Prefecture, Japan) on 21 May. This caused the collapse of the southern flank of the Mayuyama dome in front of Mount Unzen, resulting in a tremendous tsunami, killing 15,000 people altogether. It was also called Shimabara erupted, Higo affected (島原大変肥後迷惑), (Shimabara means the central mountain of the Shimabara Peninsula) since many people were killed by this tsunami in Higo (Kumamoto Prefecture, situated 20 km (12.4 mi) across the Ariake Sea).
Monroe County, Michigan
Monroe County is a county in the U.S. state of Michigan. As of the 2020 Census, the population was 154,809. The largest city and county seat is Monroe. The county was established as the second county (after Wayne County) in the Michigan Territory in 1817 and was named for then-President James Monroe. Monroe County is coterminous with the Monroe metropolitan statistical area.

Wayne County, Michigan
Wayne County is the most populous county in the U.S. state of Michigan. As of 2020, the United States census placed its population at 1,793,561, making it the 19th-most populous county in the United States. The county seat is Detroit. The county was founded in 1796 and organized in 1815. Wayne County is included in the Detroit-Warren-Dearborn, MI Metropolitan Statistical Area. It is one of several U.S. counties named after Revolutionary War-era general Anthony Wayne.