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.

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.
Leichhardt, New South Wales
Leichhardt (/laɪkɑːrt/) is a suburb in the Inner West of Sydney, in the state of New South Wales, Australia. Leichhardt is located 5 kilometres west of the Sydney central business district (CBD) and is the administrative centre for the local government area (LGA) of the Inner West Council. The suburb is bordered by Haberfield to the west, Annandale to the east, Lilyfield to the north and Petersham, Lewisham and Stanmore to the south.

Glebe, New South Wales
Glebe is an inner-western suburb of Sydney in New South Wales. Glebe is located 3 kilometres (1.9 mi) southwest of the Sydney central business district in the Inner West region.

Glebe is surrounded by Blackwattle Bay and Rozelle Bay, inlets of Sydney Harbour, in the north. The suburb of Ultimo lies to the east and the suburbs of Annandale and Forest Lodge lie to the west. The southern boundary is formed by Parramatta Road and Broadway. Broadway is a locality sited along the road of the same name, which is located on the border of Glebe, Chippendale and Ultimo.
John I Tzimiskes
John I Tzimiskes (Greek: Ἰωάννης ὁ Τζιμισκής, romanized: Iōánnēs ho Tzimiskēs; c. 925 – 10 January 976) was the senior Byzantine emperor from 969 to 976. An intuitive and successful general who married into the influential Skleros family, he strengthened and expanded the Byzantine Empire to include Thrace and Syria by warring with the Rus' under Sviatoslav I and the Fatimids respectively.

Çemişgezek
Çemişgezek (Armenian: Չմշկածագ, romanized: Čmškacag; Kurdish: Melkişî) is a municipality (belde) and seat of Çemişgezek District of Tunceli Province, Turkey. The town had a population of 3,009 in 2021 and is populated by both Kurds and Turks.

The town is divided into the neighbourhoods of Çukur, Hacı Cami, Hamamatik, Kale, Mescit, Tepebaşı and Yenimahalle.
1977 Davis Cup Americas Zone
The Americas Zone was one of the three regional zones of the 1977 Davis Cup.

14 teams entered the Americas Zone in total, with 12 teams competing in the preliminary rounds to advance to the main draw and join the previous year's finalists Chile and South Africa. The winner of the main draw went on to compete in the Inter-Zonal Zone against the winners of the Eastern Zone and Europe Zone.

Argentina defeated the United States in the final and progressed to the Inter-Zonal Zone.

1977 Davis Cup Eastern Zone
The Eastern Zone was one of the three regional zones of the 1977 Davis Cup.

12 teams entered the Eastern Zone, with 8 teams competing in the preliminary round to join the previous year's semifinalists in the main draw. India and Indonesia received byes into the quarterfinals, while Australia and New Zealand received byes into the semifinals. The winner of the main draw went on to compete in the Inter-Zonal Zone against the winners of the Americas Zone and Europe Zone.

Australia defeated New Zealand in the final and progressed to the Inter-Zonal Zone.
InterCity
InterCity (commonly abbreviated IC on timetables and tickets) is the classification applied to certain long-distance passenger train services in Europe. Such trains (in contrast to InterRegio, regional, local, or commuter trains) generally call at major stations only.

An international variant of the InterCity trains are the EuroCity (EC) trains, which consist of high-standard coaches and are run by a variety of operators.

Trans Europ Express
The Trans Europ Express, or Trans-Europe Express (TEE), was an international first-class railway service in western and central Europe that was founded in 1957 and ceased in 1995. At the height of its operations, in 1974, the TEE network comprised 45 trains, connecting 130 different cities, from Spain in the west to Austria in the east, and from Denmark to Southern Italy.
GPhoto
gPhoto is the name of a free, redistributable, ready to use set of digital camera software applications for Unix-like systems. The core functionality is provided by libgphoto2, which is a library for use in digital photography - it supports retrieving of images from camera devices, upload, and remote controlled configuration and capture, depending on whether the camera supports those features. libgphoto2 is the successor of gphoto with lots of new features and additional camera drivers.

libgphoto2 is the basis for image acquisition and camera interfacing on Linux, and is used by applications such as Darktable, DigiKam, Shotwell, Entangle, GIMP, gThumb, and others.

gPhoto2 is also the name of the command line (CLI) interface to libgphoto2. gPhoto2 and libgphoto2 have been released alongside each other with the same version number until 2.5.28.

Released under the GNU Lesser General Public License, gPhoto is free software.

GThumb
gThumb is a free and open-source image viewer and image organizer with options to edit images. It is designed to have a clean and simple user interface and follows the GNOME Human Interface Guidelines and integrates well with the GNOME desktop environment.
Modern language
A modern language (also known as a living language) is any human language that is currently in use as a native language.

The term is used in language education to distinguish between languages which are used for day-to-day communication (such as French and German) and dead classical languages such as Latin and Classical Chinese, which are studied for their cultural and linguistic value. For example, the Modern Language Association tracks student enrollments in Ancient Greek versus Modern Greek, or Biblical Hebrew versus Modern Hebrew, separately.

SIL Ethnologue defines a living language as "one that has at least one speaker for whom it is their first language" (see also Language § Linguistic diversity).

Language education
Language education refers to the processes and practices of teaching a second or foreign language. Its study reflects interdisciplinary approaches, usually including some applied linguistics. There are four main learning categories for language education: communicative competencies, proficiencies, cross-cultural experiences, and multiple literacies.
Hawk's Tor, Blisland
50°33′00″N 4°37′30″W﻿ / ﻿50.5501°N 4.6249°W﻿ / 50.5501; -4.6249

Hawk's Tor is a hill and tor on Bodmin Moor in Cornwall, England, UK. Its summit is 307 metres (1,007 ft) above sea level.

The tor, which is in the civil parish of Blisland, is located 7 miles (11 km) north east of the town of Bodmin. The slopes of the tor contain Hawkstor Downs, the Stripple stones, a stone circle and Hawkstor Pit, which is a Site of Special Scientific Interest noted for its biological interest.

There is another Hawk's Tor (329 m) on Bodmin Moor, further east, near the village of North Hill.

In 2022 the Hawks Tor reservoir, an old clay pit, was bought online by South West Water. Its volume is about 1.5 million cubic metres.

Blisland
Blisland (Cornish: Blyslann) is a village and civil parish in Cornwall, England, United Kingdom. It is approximately five miles northeast of Bodmin. According to the 2001 census, the parish had a population of 565. This had increased to 608 at the 2011 census.

The parish is entirely rural in character, the northeast being moorland and the southwest lower lying farmland. The parish is bordered to the north by St Breward parish; to the west by St Mabyn and Helland parishes; to the south by Cardinham, Warleggan, and St Neot parishes; and to the northeast by Altarnun parish.

The hamlets of Bradford, Keybridge, Merry Meeting, Pendrift, Tresarrett and Waterloo are in the parish. Blisland is sometimes said to be the only village in Cornwall with a village green, however Herodsfoot and Talskiddy are others.
2022 Heartland Championship
The 2022 Heartland Championship, was the 16th edition of the Heartland Championship, a rugby union competition involving the twelve amateur provincial unions in New Zealand.

The tournament began with a round-robin stage in which the twelve teams played eight games each, from which the top four advanced to the Meads Cup semifinals, while fifth to eighth advanced to the Lochore Cup semifinals. In both of these knockout stages the top seeds (first and fifth) played at home against the lowest seeds (fourth and eighth), the second highest seeds (second and sixth) played at home against the third highest seeds (third and seventh) and the final featured the higher seed playing at home against the lower seed.

Heartland Championship
The Heartland Championship is an annual round-robin rugby union competition in men's domestic New Zealand rugby. First played in 2006, it is the third highest level of competition in New Zealand alongside the Ranfurly Shield. It is organised by New Zealand Rugby (NZR) and since 2021, it has been known as the Bunnings Heartland Championship after Bunnings, its naming rights sponsor.

Following the 2005 National Provincial Championship the NPC was restructured into two competitions. The Heartland Championship would include semi-professional and amateur players, and consist of the bottom twelve populated and performing regional teams. The higher ranked teams would compete in the reformed professional National Provincial Championship.
B. J. Widick
B. J. Widick (born Branko J. Widick in Okučani, present-day Croatia, October 25, 1910; died Ann Arbor, Michigan, June 28, 2008) was an American labor activist in the United Auto Workers union and socialist movements.

Workers Party (United States)
The Workers Party (WP) was a Third Camp Trotskyist group in the United States. It was founded in April 1940 by members of the Socialist Workers Party who opposed the Soviet invasion of Finland and Leon Trotsky's belief that the USSR under Joseph Stalin was still innately proletarian, a "degenerated workers' state." They included Max Shachtman, who became the new group's leader, Hal Draper, C. L. R. James, Raya Dunayevskaya, Martin Abern, Joseph Carter, Julius Jacobson, Phyllis Jacobson, Albert Glotzer, Stan Weir, B. J. Widick, James Robertson, and Irving Howe. The party's politics are often referred to as "Shachtmanite."

At the time of the split, almost 40%  of the membership of the SWP left to form the Workers Party. The WP had approximately 500 members. Although it recruited among workers and youth during World War II it never grew substantially, despite having more impact than its numbers would suggest.
347th Rescue Wing
The 347th Rescue Wing is an inactive United States Air Force unit.  It was last assigned to the Air Force Special Operations Command, stationed at Moody Air Force Base, Georgia.  It was inactivated on 1 October 2006.

69th Fighter Squadron
The 69th Fighter Squadron is a United States Air Force Reserve fighter squadron.  It is assigned to the 944th Operations Group, stationed at Luke Air Force Base, Arizona.

The 69th Fighter Squadron replaced the 301st Fighter Squadron in 2010.  It trains Air Force Reserve Command pilots combat tactics with the F-16 Fighting Falcon.  It is integrated with the 56th Operations Group. The squadron flies Block 42 F-16Cs, tail code "LF", 69th FS carrying a black tail band.
Shuangpai County
Shuangpai County (simplified Chinese: 双牌县; traditional Chinese: 雙牌縣; pinyin: Shuāngpái Xiàn) is a county in Hunan Province, China, it is under the administration of the prefecture-level city of Yongzhou. Shuangpai is also the 3rd smallest administrative unit (after Shaoshan and Guzhang)  by population in the counties and county-level cities of the province.

Located on the southern margin of the province, it is adjacent to the city proper of Yongzhou, and lies to the eastern border of Guangxi. The county is bordered to the north and the northwest by Lingling District, to the east and the southeast by Ningyuan County, and to the southwest and the south by Dao County, Quanzhou County of Guangxi. Shuangpai County covers an area of 1,751 km2 (676 sq mi), and as of 2015, it had a permanent resident population of 202,400. The county has 6 towns and 5 townships under its jurisdiction, and the county seat is Shuangbo (泷泊镇).

Lingling, Yongzhou
Lingling District is one of two urban districts of Yongzhou City, Hunan Province, China. It is located on the south of the city proper,  and lies to the eastern border of Guangxi.

The district is bordered to the north by Dong'an County and Lengshuitan District, to the east by Qiyang County, to the south by Shuangpai County, and to the west by Quanzhou County of Guangxi. Lingling District covers an area of 1,962 km2 (758 sq mi), and as of 2015, It had a registered population of 622,400. Lingling District has four subdistricts, 7 towns and 3 townships under its jurisdiction, and the government seat is Xujiajing (徐家井街道).
Leif Arrhenius
Leif Hilding Arrhenius (born 15 July 1986) is a professional American-Swedish athlete competing in the shot put and discus throw. He represented Team Sweden at two World and three European Championships. In addition, he is the 2011 U.S. Collegiate Indoor Champion.

BYU Cougars
The BYU Cougars are the intercollegiate athletic teams that represent Brigham Young University (BYU), located in Provo, Utah. BYU fields 21 National Collegiate Athletic Association (NCAA) varsity athletic teams. They are a member of the Big 12 Conference for all sports except men's volleyball which is a member of the Mountain Pacific Sports Federation.
Lapplandsender
Lapplandsender (German: Soldatensender Lappland) was a World War II military radio station for Nazi German forces in Northern Finland and Northern Norway. The transmitter was in the German garrison area outside the provincial capital of Rovaniemi in the Arctic Circle. The station was under command of Propagandakompanie 680, which was one of the propaganda units of the Wehrmacht, the German army.

Lapplandsender broadcast entertainment, news and propaganda daily from December 1941. In October 1944, during their retreat from Lapland, the Germans took the station down and moved it to Bergen in Western Norway. Shortly afterwards, Rovaniemi was burned to the ground during the course of the Battle of Rovaniemi.

Battle of Rovaniemi
The Battle of Rovaniemi was an event during the 1944 Lapland War. The actual fighting between the components of the Finnish Armoured Division and Finnish 3rd Division against the troops of the German Twentieth Mountain Army took place at the vicinity of the town of Rovaniemi. The notoriety of the encounter derives from the near-total destruction of the town.
Sayaka Matsumoto
Sayaka Matsumoto (サヤカ・松本; born December 5, 1982) is a Japanese-born American judoka. Matsumoto competed for the United States in the women's 48 kg judo event at the 2008 Summer Olympics.

Matsumoto, who was raised in California, is coached by her father, David Matsumoto. She began judo at the age of 5. Matsumoto won the 2004 U.S. Olympic Trials, but did not compete in the Olympics that year because the U.S. failed to earn a spot in her weight class. Matsumoto again won the U.S. Olympic Trials in 2008 and competed in the Olympic Games.

At the 2008 Summer Olympics she fought against Ryoko Tani (JPN) and Wu Shugen (CHN), but lost both matches.

Wu Shugen
Wu Shugen (Mongolian: Ündes; born 26 August 1987 in Inner Mongolia) is a female Mongol judoka from China who competed at the 2008 Summer Olympics and 2012 Summer Olympics in the Extra lightweight (under 48 kg) event. At the 2008 Summer Olympics, she lost in the quarterfinals to Ryoko Tani.  In the repechage she beat Sayaka Matsumoto, before losing to Paula Pareto.  She beat Lisa Kearney before losing to Sarah Menezes in the 2012 Summer Olympics.  In the repechage she lost to Éva Csernoviczki.
Oregon Route 99
Oregon Route 99 is a state highway that runs between the southern border of Oregon, and the city of Junction City. Oregon Route 99 was formed from parts of the former U.S. Route 99; it shares much of its route with I-5, but much of it is also independent. Between Portland and Junction City, the highway is forked into two routes: Oregon Route 99E and Oregon Route 99W.

Oregon Route 234
Oregon Route 234 is an Oregon state highway which runs between the city of Gold Hill, Oregon and the town of Eagle Point.  Known as the Sams Valley Highway No. 271, it extends for 18 miles (29 km), entirely within Jackson County.
Saxon revolt of 1077–1088
The Saxon revolt was a civil war fought between 1077 and 1088, early in the history of the Holy Roman Empire. The revolt was led by a group of opportunistic German princes who elected as their figurehead the duke of Swabia, Rudolf of Rheinfeld, who became the anti-king. Rudolf was a two-way brother-in-law of the young King Henry IV of Germany, who had been crowned at the age of six and had taken the reins of power at age sixteen. The Great Revolt followed the Saxon Rebellion of 1073–75.

Welf I, Duke of Bavaria
Welf I (c. 1035/1040 – 6 November 1101) was Duke of Bavaria from 1070 to 1077 and again from 1096 until his death. He was the first member of the House of Welf branch of the House of Este. In the genealogy of the Elder House of Welf, he is counted as Welf IV or simply Guelf.
Estes Park, Colorado
Estes Park (/ˈɛstɪs/) is a statutory town in southwestern Larimer County, Colorado, United States. The town population was 5,904 at the 2020 United States census. Estes Park is a part of the Fort Collins, CO Metropolitan Statistical Area and the Front Range Urban Corridor. A popular summer resort and the location of the headquarters for Rocky Mountain National Park, Estes Park lies along the Big Thompson River. Landmarks include The Stanley Hotel and The Baldpate Inn. The town overlooks Lake Estes and Olympus Dam.

Seven Keys Lodge
Seven Keys Lodge (formerly known as The Baldpate Inn) is a historic hotel located in Estes Park, Colorado. It has designations on the National Register of Historic Places and the Colorado State Register of Historic Properties. The property has changed hands several times, always under a private family's proprietorship. In 2020, the property was purchased and the new owners changed the name to the Seven Keys Lodge.
United States of Venezuela
The United States of Venezuela (Spanish: Estados Unidos de Venezuela) was the official name of Venezuela, which adopted in its 1864 constitution under the Juan Crisóstomo Falcón government. This remained the official name until 1953, when the constitution of that year renamed it the Republic of Venezuela. In 1999 under newly elected president Hugo Chávez and his modification to the Constitution, Venezuela's official name became the Bolivarian Republic of Venezuela.

Constitution of Venezuela (1891)
The Constitution of Venezuela of 1891 (Official name: Constitution of the United States of Venezuela. Spanish: Constitución de los Estados Unidos de Venezuela) was a Constitution subscribed by all the members of the National Legislature on April 9, 1891, mainly promoted by President Raimundo Andrueza Palacios. It had 8 titles, each with 1 or 7 sections, and a total of 122 articles, among which the following stand out:
Taya Valkyrie
Kira Renée Magnin-Forster (born October 22, 1983), better known by her ring name Taya Valkyrie, is a Canadian professional wrestler, fitness competitor, and model. She is signed to All Elite Wrestling (AEW), where she is a member of MxM TV. She also wrestles in AEW's sister promotion Ring of Honor (ROH). Valkyrie is best known for her time in Lucha Libre AAA Worldwide (AAA), where she is a record-tying 4-time AAA Reina de Reinas Champion (with her first reign being the longest in the title's history at 945 days), and Impact Wrestling, where she is a former one-time and longest-reigning Impact Knockouts Champion and a two-time Impact Knockouts World Tag Team Champion. She briefly wrestled for WWE under the ring name Franky Monet.

Kamille (wrestler)
Kailey Dawn Latimer (born October 24, 1992), better known by her ring name Kamille, is an American professional wrestler and former softball player, arena football player, and bodybuilder. As of February 2024, she is signed to All Elite Wrestling (AEW). She is best known for her time with the National Wrestling Alliance (NWA) from 2018 to 2024, where she is a former one-time NWA World Women's Champion. She also performed in Lucha Libre AAA Worldwide from 2022 to 2023.
Dieng temples
Dieng temples (Indonesian: Candi Dieng) are a group of 7th and/or eighth-century Hindu candi or temple compounds located in Dieng Plateau, near Banjarnegara, Central Java, Indonesia. These edifices originate from the Kalingga Kingdom.: 79, 90   The plateau is home to eight small Hindu temples that are among the oldest surviving religious structures ever built in Java and the earliest Hindu temples in Indonesia.  The temples show many features of Indian Hindu temple architecture.

The real name of the temples, the history, and the king responsible for the construction of these temples were unknown. This is because of the scarcity of data and inscriptions connected to the construction of these temples. The local Javanese population named each temple according to Javanese wayang characters, mostly taken from the Mahabharata epic.

The Kailasa museum nearby contains many pieces of sculpture removed from the temples.

Dieng Plateau
The Dieng Plateau, often called simply Dieng (Javanese: ꦣꦶꦲꦾꦁ; Javanese pronunciation: [dijénɡ]) is a plateau in Central Java, Indonesia that forms the floor of the caldera complex on the Dieng Volcanic Complex. Administratively, this plateau is included in the territory of Banjarnegara Regency and Wonosobo Regency. It covers agricultural areas that have a subtropical climate with high levels of rainfall.

Dieng is surrounded by a series of mountains that stretch about 6 km (4 miles) from north to south and 14 km (9 miles) from west to east. Dieng is the highest plateau on the island of Java, having an average elevation of more than 2,100 meters above sea level.
Australian & New Zealand Handgun
Australian & New Zealand Handgun is a publication of the Sporting Shooters' Association of Australia, specifically dealing with the sport shooting, professional use, and historic study of handguns in Australia.

Sporting Shooters Association of Australia
The Sporting Shooters' Association of Australia (SSAA) is a federated non-government organisation established in 1948 as a representative body to promote shooting sports and protect the legal rights and interests of firearm owners in Australia. As of 2022 the SSAA has a membership of around 218,000. In addition to the state branches overseeing various clubs and gun ranges, SSAA also has a national political lobbying department and an insurance arm. State branches run local- and state-level shooting competitions, while the SSAA also coordinates competitions at the national and international levels.