hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Direct product of groups
In mathematics, specifically in group theory, the direct product is an operation that takes two groups G and H and constructs a new group, usually denoted G × H.  This operation is the group-theoretic analogue of the Cartesian product of sets and is one of several important notions of direct product in mathematics.

In the context of abelian groups, the direct product is sometimes referred to as the direct sum, and is denoted .  Direct sums play an important role in the classification of abelian groups: according to the fundamental theorem of finite abelian groups, every finite abelian group can be expressed as the direct sum of cyclic groups.

Direct product
In mathematics, a direct product of objects already known can often be defined by giving a new one. That induces a structure on the Cartesian product of the underlying sets from that of the contributing objects. The categorical product is an abstraction of these notions in the setting of category theory.

Examples are the product of sets, groups (described below), rings, and other algebraic structures. The product of topological spaces is another instance.

The direct sum is a related operation that agrees with the direct product in some but not all cases.
Paszęcin
Paszęcin [paˈʂɛnt͡ɕin] (German: Passentin) is a village in the administrative district of Gmina Rąbino, within Świdwin County, West Pomeranian Voivodeship, in north-western Poland. It lies approximately 4 km (2 mi) south-east of Rąbino, 15 km (9 mi) north-east of Świdwin, and 103 km (64 mi) north-east of the regional capital Szczecin.

For the history of the region, see History of Pomerania.

The village has a population of 210.

Gmina Rąbino
Gmina Rąbino is a rural gmina (administrative district) in Świdwin County, West Pomeranian Voivodeship, in north-western Poland. Its seat is the village of Rąbino, which lies approximately 15 kilometres (9 mi) north-east of Świdwin and 103 km (64 mi) north-east of the regional capital Szczecin. The gmina covers an area of 180.00 square kilometres (69.5 sq mi), and as of 2006 its total population is 3,935.
The Harmonies
The Harmonies are a five-piece girlband formed in 2010, with the finalists of a competition with over 200,000 contestants organised by the Women's Institute and announced in February 2010, to create an album in celebration of the 95th anniversary of the WI.

Women's Institute
The Women's Institute (WI) is a community-based organization for women in Canada, the United Kingdom, South Africa and New Zealand. The movement was founded in Stoney Creek, Ontario, Canada, by Erland and Janet Lee with Adelaide Hoodless being the first speaker in 1897. It was based on the British concept of Women's Guilds, created by Rev. Archibald Charteris in 1887 and originally confined to the Church of Scotland. From Canada, the organization spread back to Britain, throughout the British Empire and Commonwealth, and to other countries. Many WIs belong to the Associated Country Women of the World organization.
Protocol of Sèvres
The Protocol of Sèvres (French, Protocole de Sèvres) was a secret agreement reached between the governments of Israel, France, and the United Kingdom during discussions held between 22 and 24 October 1956 in Sèvres, France. The protocol concerns their joint political and military collusion to topple the Egyptian leader Colonel Gamal Abdel Nasser, by invading and occupying the Suez Canal zone in response to President Nasser's nationalization of the Suez Canal on 26 July. The planning for and the agreements contained in the protocol began the Suez Crisis on 29 October 1956.

Sèvres
Sèvres (/ˈsɛvrə/, French: [sɛvʁ(ə)] ⓘ) is a French commune in the southwestern suburbs of Paris. It is located 9.9 kilometres (6.2 miles) from the centre of Paris, in the Hauts-de-Seine department in the Île-de-France region. As of 2023, the population of the commune was 22,303. The commune is known for its famous porcelain production at the Manufacture nationale de Sèvres, which was also where the Treaty of Sèvres (1920) was signed.
Richie Cummins
Richie Cummins (born 1991 in Gort, County Galway) is an Irish sportsman. He plays hurling with his local club Gort and was a member of the Galway minor inter-county team from 2008 until 2009. Cummins captained Galway to the All-Ireland minor title in 2009.

Gort GAA
Gort GAA Club is a Gaelic games club located in Gort, County Galway, Ireland. It is a member of the Galway branch of the Gaelic Athletic Association (GAA). Founded at the turn of the 20th century, the club is almost exclusively concerned with the sport of hurling.

The club competes in competitions run by Galway GAA, and has won the Galway Senior Hurling Club Championship and Connacht Senior Club Hurling Championship on several occasions.
Sad Robots
Sad Robots is an EP released by the Canadian band Stars. It was released on September 1, 2008 on digital download.  It is also available as a physical CD through their website, as well as during their fall 2008 tour. The album cover and merchandise for Stars' 2008–9 tour features the comic robot character Boilerplate.

Stars (Canadian band)
Stars is a Canadian indie pop/rock band based in Montreal, Quebec. Since forming in 2000, they have released nine albums and a number of EPs. Their music has been nominated for two Juno Awards and two Polaris Music Prizes.
Lok Nayak Hospital
Lok Nayak Hospital (Hindi: लोक नायक अस्पताल), formerly known as Irwin Hospital till November 1977, then changed to Lok Nayak Jaya Prakash Hospital (LNJP) in the honour of Jayaprakash Narayan, Indian independence activist and politician. It is maintained and run by the Health and Family Welfare Department, Government of Delhi.

Jayaprakash Narayan
Jayaprakash Narayan Srivastava (listenⓘ; 11 October 1902 – 8 October 1979), also known as JP and Lok Nayak (Hindi for "People's leader"), was an Indian politician, theorist and independence activist. He is mainly remembered for leading the mid-1970s opposition against Prime Minister Indira Gandhi and calling for her overthrow in a "total revolution". In 1999, Narayan was posthumously awarded the Bharat Ratna, India's highest civilian award, in recognition of his social service. His other awards include the Ramon Magsaysay Award for public service in 1965.
Drumkeen
Drumkeen (Irish: Droim Caoin, meaning 'beautiful ridge') is a village and townland in County Donegal, Ireland. The village is near the N13 primary road, about 8 kilometres (5 mi) west of Convoy. The village population was 333 at the 2022 census. The local soccer club, Drumkeen United, play at St Patrick's Park. The village is located just above the Burn Dale, which flows along the southern edge of the village. Drumkeen is the 660th biggest town-land and has an area of 2.2662 km2.

N13 road (Ireland)
The N13 road is a national primary road in Ireland, running in County Donegal in Ulster from Stranorlar to just outside Derry. This road connects Letterkenny to Sligo, Derry and onwards to other destinations.
DPGC: U Know What I'm Throwin' Up
DPGC: U Know What I'm Throwin' Up is the fourth solo studio album by American rapper and record producer Daz Dillinger. It was released on May 6, 2003 via Gangsta Advisory Records, making it his first album for the label. Production was handled by Soopafly, Fredwreck, Shon Don, Def Jef, Meech Wells, Mike Smoove, Quaze, and Daz himself, who also served as executive producer. It features guest appearances from Snoop Dogg, Soopafly, Shon Don, Bad Azz, Crystal, E-White, Goldie Loc, Uncle Reo and Whiteboy. The album did not reach the Billboard 200, however it peaked at number 35 on the Top R&B/Hip-Hop Albums and number 13 on the Independent Albums charts in the United States.

The album contains multiple diss tracks aimed at Death Row Records, its chief executive officer Suge Knight, ex-Tha Dogg Pound groupmate Kurupt who re-signed himself with the label, Crooked I and other Death Row affiliates, as well as Ja Rule and Benzino.

Gangsta Advisory Records
Gangsta Advisory Records is the independent record label headed by Daz Dillinger. Some sources state the hierarchy of Daz's labels were flipped 2003 by ordering D.P.G. Recordz under G.A.R. to become its subsidiary and endorsing all license rights of D.P.G.
Barnala railway station
Barnala (station code: BNN) is a railway station located in Barnala district in the Indian state of Punjab and serves Barnala city which is the administrative headquarter of the district. Barnala station falls under Ambala railway division of Northern Railway zone of Indian Railways.

Barnala
Barnala is a city and the administrative headquarters of Barnala district in the Indian state of Punjab. Located in the Malwa region, it serves as a key agricultural and trading hub, surrounded by fertile plains. As of the 2011 census, the city had a population of 116,449, while the district's population was 595,527. Estimates for 2024 project the district population at approximately 839,694, reflecting steady growth driven by rural-urban migration and agricultural prosperity. The city is renowned for its role in Punjab's textile and agro-machinery industries, earning it the nickname "Manchester of Punjab" due to its textile mills. Barnala district was carved out of Sangrur district on 19 November 2006, making it Punjab's 23rd district at the time.
Adalita (album)
Adalita is the debut studio album by Australian musician Adalita.  It was released by Liberation Music in March 2011. It received the Australian Independent Record (AIR) Award for 'Best Independent Album' in 2011.

Adalita Srsen
Adalita Srsen (/ˈsɜːrsən/, born 25 February 1971), known mononymously as Adalita, is an Australian rock musician who is a founding member of the rock bands Magic Dirt and Bleak Squad, as well as a solo artist. She released her first solo album, Adalita, in 2011 and her second solo album, All Day Venus, in September 2013.
Mount Vernon, Washington
Mount Vernon is the county seat of and the most populous city in Skagit County, Washington, United States. A central location in the Skagit River Valley, the city is located 51 miles (82 km) south of the Canadian border and 60 miles (97 km) north of Seattle. The population was 35,219 at the 2020 census, making it the 35th most-populous city in Washington, with 62,966 people living in its urban area. It is one of two principal cities of and included in the Mount Vernon-Anacortes Metropolitan Statistical Area, covering most of Skagit County.

Mount Vernon and its surrounding areas are known for its annual Skagit Valley Tulip Festival, which has Mount Vernon host a street fair in downtown once a year, with millions of tulips grown in the Skagit Valley every year. Between the 2000 and 2020 census, Mount Vernon grew by 34.3%, and is a prominent location in Northwestern Washington, connected to neighboring communities via I-5 and Amtrak (with Skagit Station).

Ross Mathews
Ross Mathews (born September 24, 1979) is an American television host and personality. He rose to fame as "Ross the Intern" as a correspondent for The Tonight Show with Jay Leno.

Mathews has appeared on Chelsea Lately, Celebrity Fit Club, The Insider, Celebrity Big Brother as well as his own talk show Hello Ross. Ross is currently an executive producer and judge on RuPaul's Drag Race and co-hosts The Drew Barrymore Show with Drew Barrymore.
Grunewald Tower
The Grunewald Tower or Grunewaldturmⓘ is a historical tower in the Grunewald forest of southwestern Berlin, Germany, built in 1897-99 according to plans designed by Franz Heinrich Schwechten. The viewing platform offers a view over the Havel at a height of 36 metres (118 ft).

Grunewald (forest)
Grunewald (German pronunciation: [ˈɡʁuːnəˌvalt] ⓘ) is a German forest located in the western side of Berlin on the east side of the Havel, mainly in the Grunewald locality. At 3,000 hectares (7,400 acres) it is the largest green area in the city of Berlin.
Baal-gad
Baal-Gad was a Canaanite town at the foot of Mount Hermon. It is mentioned in the Bible three times, all of them in the Book of Joshua (Josh. 11:17; 12:7; 13:5). In all cases, it is described as the northernmost point of Joshua's conquests. The name may relate to Gad, a Semitic deity of fortune, but more likely simply refers to Baal with the epithet “of fortune”.

Gad (deity)
Gad was the name of the pan-Semitic god of fortune, usually depicted as a male but sometimes as a female, and is attested in ancient records of Aram and Arabia. Gad is also mentioned in the Bible as a deity in the Book of Isaiah (Isaiah 65:11 – some translations simply call him (the god of) Fortune), as having been worshipped by a number of Hebrews during the Babylonian captivity. Gad apparently differed from the god of destiny, who was known as Meni. The root verb in Gad means cut or divide, and from this comes the idea of fate being meted out.
Le jongleur de Notre-Dame (opera)
Le jongleur de Notre-Dame is a three-act opera (labelled in the programme as Miracle in Three Acts) by Jules Massenet to a French libretto by Maurice Léna. It was first performed at the Opéra Garnier in Monte Carlo on 18 February 1902. It is one of five operas Massenet set in the Middle Ages, the others being Le Cid (1885), Esclarmonde (1889), Grisélidis (1901), and Panurge (1913).

Lucien Fugère
Lucien Fugère (French pronunciation: [lysjɛ̃ fyʒɛʁ]; 22 July 1848, Paris – 15 January 1935, Paris) was a French baritone, particularly associated with the French repertory and Mozart roles. He enjoyed an exceptionally long career, singing into his 80s.
Felice Cece
Felice Cece (26 March 1936 – 12 May 2020) was an Italian Roman Catholic archbishop.

Cece was born in Italy and was ordained to the priesthood in 1959. He served as bishop of the Roman Catholic Diocese of Teano-Calvi, Italy, from 1984 to 1989 and as archbishop of the Roman Catholic Archdiocese of Sorrento-Castellammare di Stabia, Italy, from 1989 to 2010.

Archdiocese of Sorrento-Castellammare di Stabia
The Archdiocese of Sorrento-Castellammare di Stabia (Latin: Archidioecesis Surrentina-Castri Maris o Stabiensis) is a Latin archdiocese of the Catholic Church in Campania, has existed in its current form since 1986. It is a suffragan of the Archdiocese of Naples, having lost its status as a metropolitan in 1979. The Diocese of Castellammare di Stabia was suppressed, and its territory united with the Archdiocese of Sorrento, in 1986.  In 2014, in the diocese of Sorrento there was one priest for every 1,503 Catholics.
Cox's Bazar bus terminal
Cox's Bazar Bus Terminal is the central bus terminal for Cox's Bazar District. It is situated in Larpara which is outside of the border of Cox's Bazar, Bangladesh. It was established in 2001 to resolve traffic jam issues in the city which is maintained by the municipality authorities.

The terminal is closed after 5 pm even though it has to be open 24 hours a day. A number of multi-storey illegal shops have been built in front of the terminal where illegal drug trade takes place. Buses are parked outside the terminal as no parking space is available in the terminal caused by the illegal shops. Traffic jams have thus increased in the area. The terminal is in disuse due to illegal counters for long-distance buses in the city's Kolatoli Square.

On 24 January 2020, a LPG station was opened at the terminal. The terminal renovation and modernization project was inaugurated on the same date.

Cox's Bazar
Cox's Bazar is a city, fishing port, tourism centre, and the headquarters of the Cox's Bazar District and Cox's Bazar Sadar Upazila in south-eastern Bangladesh. The city has a population of about 196,000 making it the 26th largest city in Bangladesh. Cox's Bazar Beach is a major tourist attraction.
Berlin Frankfurter Allee station
Berlin Frankfurter Allee is a railway station situated on Frankfurter Allee in the Friedrichshain district of Berlin, close to the district's border with Lichtenberg. It is served by the S-Bahn lines S41, S42 (the ringbahn), S8, S85 and the U-Bahn line U5.

U5 (Berlin U-Bahn)
U5 is a line on the Berlin U-Bahn. It runs from Hauptbahnhof in Mitte eastwards through Alexanderplatz, Friedrichshain, Lichtenberg and Friedrichsfelde, surfaces in Biesdorf-Süd to pass Kaulsdorf and Hellersdorf above ground and finally reaches city limits at Hönow.
October (novel)
October  is a 2014 novel by Zoë Wicomb. Wicomb, who won a 2013 Windham–Campbell Literature Prize, is originally from Namaqualand, South Africa, and is an emeritus professor at the University of Strathclyde.

October is the story of Mercia Murray, a professor in Glasgow, Scotland, who returns to Kliprand, Namaqualand in South Africa when her brother, Jake, writes her to come home and get his son, Nicky. The themes include homemaking, exile, return and race. Quadrapheme: 21st Century Literature has noted that October is a story about homecoming, a story about home, a story about belonging, not-belonging, women and children, class and race and education, motherhood and fatherhood.

Asked by  Anna James to sum up the book in three words, Zoë Wicomb answered, "Home, deracination, family secrets."

Zoë Wicomb
Zoë Charlotte Wicomb (23 November 1948 – 13 October 2025) was a South African author and academic who lived in the United Kingdom from the 1970s until her death. Her 1987 debut book, You Can't Get Lost in Cape Town – a collection of inter-related short stories, set during the Apartheid era and partly autobiographical – received wide praise, and in 2000 was described by Toni Morrison as "seductive, brilliant and precious".

In 2013, Wicomb was awarded the inaugural Windham–Campbell Literature Prize for her fiction.
William John Read
William John (Jack) Read (born 18 September 1905, Hobart, Tasmania, Australia; died 29 June 1992, Ballarat, Victoria (Australia)), was an Australian Coastwatcher on Bougainville Island in New Guinea during World War II. He was awarded the Distinguished Service Cross by the United States for his service during World War II in the Solomon Islands campaign and the New Guinea campaign. His experiences and reports have become an important source for historians regarding the history of the coastwatchers.

Coastwatchers
The Coastwatchers, also known as the Coast Watch Organisation, Combined Field Intelligence Service or Section C, Allied Intelligence Bureau, were Allied military intelligence operatives stationed on remote Pacific islands during World War II to observe enemy movements and rescue stranded Allied personnel. They played a significant role in the Pacific Ocean theatre and South West Pacific theatre, particularly as an early warning network during the Guadalcanal campaign.
Michel Rocard
Michel Rocard AC OQ (French: [miʃɛl ʁɔkaʁ]; 23 August 1930 – 2 July 2016) was a French politician and a member of the Socialist Party (PS). He served as Prime Minister under François Mitterrand from 1988 to 1991 during which he created the Revenu minimum d'insertion (RMI), a social minimum welfare program for indigents, and achieved the Matignon Accords regarding the status of New Caledonia. He was a member of the European Parliament, and was strongly involved in European policies until 2009. In 2007, he joined a Commission under the authority of Nicolas Sarkozy's Minister of Education, Xavier Darcos.

Yvelines
Yvelines (French pronunciation: [ivlin] ⓘ) is a department in the western part of the Île-de-France region in Northern France. In 2019, it had a population of 1,448,207. Its prefecture is Versailles, home to the Palace of Versailles, the principal residence of the King of France from 1682 until 1789, a UNESCO World Heritage Site since 1979. Yvelines' subprefectures are Saint-Germain-en-Laye, Mantes-la-Jolie and Rambouillet.
5FM
5FM is a South African FM radio station forming part of the South African Broadcasting Corporation (SABC), South Africa's public broadcaster. 5FM follows a Top 40 music format aimed at a youth market, together with news and sports coverage.

Originally named Radio 5, the station was re-branded as "5FM" in 1992, and has as its current logo a red "5" and superscripted "FM" within a circle and the words "The Power of" inscribed along the upper periphery of the circle.

The station is currently managed by Masixole Mdingane, Business Unit Manager of the PCS Combo (Good Hope FM & 5FM).

Thando Thabethe
Thando Thabethe (born 18 June 1990) is a South African actress,  and Radio DJ who was the presenter for the television show Thando Bares All on channel TLC and current drive time host on 947. She is Nivea's first brand ambassador in Africa.  In 2019, Thando was named one of Forbes Africa's 30 Under 30. She is also the host of 947 Drive With Thando.
RAF Syerston
Royal Air Force Syerston, commonly known simply as RAF Syerston (ICAO: EGXY), is a Royal Air Force station in the parish of Flintham, near Newark, Nottinghamshire, England.  Opened in 1940, it was used by the Royal Air Force (RAF) as a bomber base during the Second World War, operating Vickers Wellingtons, Avro Manchesters, and the Avro Lancaster heavy bombers. Post-war, it became home to Jet Provosts of the 2 Flying Training School.  It is now home to the Royal Air Force Central Gliding School.

Flintham
Flintham is a village and civil parish in the Rushcliffe district in Nottinghamshire, 7 miles (11 km) from Newark-on-Trent and opposite RAF Syerston on the A46. It had a population of 597 at the 2011 census, estimated at 586 in 2019, and a fall to 563 at the 2021 census. The village name was taken by the Ham class minesweeper HMS Flintham.
Seibu 30000 series
The Seibu 30000 series (西武30000系) is an electric multiple unit (EMU) train type operated by the private railway operator Seibu Railway on commuter services in the Tokyo area of Japan. First introduced in April 2008, a total of six 10-car sets, eighteen 8-car sets, and six 2-car sets were built by Hitachi Rail between 2008 and 2016 to replace older three-door 101 series and 301 series sets. It is nicknamed the "Smile Train" (スマイルトレイン, Sumairu Torein).

Seibu Shinjuku Line
The Seibu Shinjuku Line (西武新宿線, Seibu-Shinjuku-sen) is a Japanese railway line owned by the private railway operator Seibu Railway, connecting Seibu Shinjuku Station in Shinjuku, Tokyo with Hon-Kawagoe Station in Kawagoe, Saitama.

The Shinjuku Line is one of two main lines of the Seibu Railway system along with the Ikebukuro Line. The two main lines cross at Tokorozawa Station in Tokorozawa, Saitama. The line serves the western suburbs of Tokyo, connecting them to Shinjuku and other areas of downtown Tokyo.
Creswell railway station
Creswell railway station serves the village Creswell in Derbyshire, England. The station is on the Robin Hood Line between Nottingham and Worksop. It is also the nearest station to the larger village of Clowne.

Creswell, Derbyshire
Creswell is a village located in the Bolsover district of Derbyshire, England. At the 2011 Census population details were included in the civil parish of Elmton-with-Creswell.  Today it is best known for Creswell Crags and its model village.  Elmton Common is an area of allotments for the township of Creswell. The village was a mining village.

Local Government services are provided by Elmton-with-Creswell Parish Council, Bolsover District Council and Derbyshire County Council.