In mathematics in group theory, the concept of a semidirect product is a generalization of a direct product. There are two related concepts of semidirect product: an inner semidirect product is a particular way in which a group can be made up of two subgroups, one of, a normal subgroup. An outer semidirect product is a way to construct a new group from two given groups by using the Cartesian product as a set and a particular multiplication operation; as with direct products, there is a natural equivalence between inner and outer semidirect products, both are referred to as semidirect products. For finite groups, the Schur–Zassenhaus theorem provides a sufficient condition for the existence of a decomposition as a semidirect product. Given a group G with identity element e, a subgroup H, a normal subgroup N ◁ G. For every g ∈ G, there are unique n ∈ h ∈ H such that g = nh. For every g ∈ G, there are unique h ∈ n ∈ N such that g = hn; the composition π ∘ i of the natural embedding i: H → G with the natural projection π: G → G/N is an isomorphism between H and the quotient group G/N.

There exists a homomorphism G → H, the identity on H and whose kernel is N. In other words, there is a split exact sequence 1 → N → G → H → 1 of groups. If any of these statements holds, we say G is the semidirect product of N and H, written G = N ⋊ H or G = H ⋉ N, or that G splits over N. To avoid ambiguity, it is advisable to specify, the normal subgroup. To introduce the notion of outer semidirect products, let us first consider the inner semidirect product. In this case, for a group G, consider its normal subgroup N and the subgroup H. Let Aut denote the group of all automorphisms of N, a group under the composition. Construct a group homomorphism φ: H → Aut defined by conjugation φ = hnh−1 for all h in H and n in N; the expression φ is written as φh for brevity. In this way we can construct a group G ′ = with group operation defined as ⋅ = = for n1, n2 in N and h1, h2 in H. Together N, H, φ determine G up to isomorphism, as we will show later. We can construct group G from its subgroups, this kind of construction is called inner semidirect product.

Let us now consider the outer semidirect product. Given any two groups N and H and a group homomorphism φ: H → Aut, we can construct a new group N ⋊φ H, called the semidirect product of N and H with respect to φ, defined as follows; this defines a group in which the identity element is and the inverse of the element is. Pairs form a normal subgroup isomorphic to N, while pairs form a subgroup isomorphic to H; the full group is a semidirect product of those two subgroups in the sense given earlier. Conversely, suppose that we are given a group G with a normal subgroup N and a subgroup H, such that every element g of G may be written uniquely in the form g = nh where n lies in N and h lies in H. Let φ: H → Aut be the homomorphism given by φ h = h n h − 1 for all n ∈ N, h ∈ H. G is isomorphic to the semidirect product N ⋊φ H; the isomorphism λ: G → N ⋊φ H is well defined by λ = λ = due to the uniqueness of the decomposition a = nh. In G, we have = n 1 h 1 n 2 h 2 = Thus, for a = n1h1 and b = n2h2 we obtain λ ( a b

Miroljub Stanković was a politician in Serbia. He served in the National Assembly of Serbia from 2014 until his death as a member of the Party of United Pensioners of Serbia. Stanković worked at the Educational Correctional Centre at Kruševac. Stanković joined the PUPS on its formation in 2005 and served on its main board from until his death, he became president of the party's municipal organization in Niš in 2010 and was a party vice-president. The PUPS was aligned with the Socialist Party of Serbia from 2008 to 2016 and fielded candidates on its electoral lists during this period. Stanković was awarded the thirty-fourth position on the Socialist-led list in the 2014 Serbian parliamentary election and was elected when the list won forty-four mandates; the Socialists participated in the coalition government, formed after the election, the PUPS provided support for the administration in the assembly. For the 2016 Serbian parliamentary election, the PUPS formed a new electoral alliance with the Serbian Progressive Party.

Stanković received the 100th position and was re-elected when the list won a majority victory with 131 out of 250 mandates. Stanković served on the assembly committee on Metohija, he had one of the best attendance records in the assembly but only spoke once, in October 2014, when he complained about the lack of heat in the assembly room

Ali Nikzad is an Iranian conservative politician and academic and a former cabinet minister. Nikzad was born in 1961, he holds a bachelor's degree in urban development from the University of Elm-va-san'at. He received his master's degree in public management from Industrial Management University. Akbar Nikzad his brother is the former Governor of Ardabil Province. Nikzad was appointed governor of Ardabil Province in 2005, he was the director of the municipalities organization at the ministry of interior until 2009. He served as the minister of transportation and housing from August 2009 to June 2011, he was acting minister of roads and transportation from February to June 2011. As minister of housing, he replaced Mohammad Saeedikia after President Mahmoud Ahmadinejad was reelected. On 7 February 2011, Nikzad was appointed by Ahmadinejad as acting minister of roads and transportation to succeed former dismissed Minister Hamid Behbahani. Nikzad was appointed minister of infrastructural affairs in May 2011 when the ministry was created, combining the two ministries of housing and urban development and road and transportation.

At the end of 2012, he was appointed acting minister of communications and information technology. President Ahmedinejad proposed him as minister for the post in January 2013. However, he was not approved by the Majlis, he announced his candidacy for the 2013 presidential election. However, he declined his candidacy. In June 2013, Nikzad was nominated as a candidate for Tehran mayor; the "Viva Spring" group consisting of Ahmedinejad's allies could not win the local elections, held on 14 June 2013 as the presidential election. Therefore, Nikzad's election as Tehran mayor became unlikely. In 2017 election, he was appointed as campaign chairman of presidential candidate Ebrahim Raisi

Joseph Albert Walding was a New Zealand politician of the Labour Party. He represented the Palmerston North for several terms. After his retirement from Parliament, he became High Commissioner to the United Kingdom, but died within months of taking the post. Walding was born in Christchurch, in 1926, he went to school in that city. When he was 15, he joined the New Zealand Merchant Navy and the British Merchant Navy; the impressions that he gained through the war shaped his outlook on life. He became a carpenter after the war, he married Eileen Norma Walding of Feilding in 1950. They had six daughters. After the marriage, the couple moved to Palmerston North. Walding joined his mother's catering business and Walding. Together with his brother Charlie, he developed the company into a successful venture. In 1957, Walding established Prepared Foods Co Ltd, a gourmet food and canning business with an export focus. Walding was first elected to Palmerston North City Council in 1959, he was re-elected in 1962 and 1965.

Having been elected to Parliament in 1967, he did not stand for the City Council again in 1968. Walding stood unsuccessfully against Bill Brown for the Palmerston North seat in the 1966 election. Following Brown's sudden death in 1967, Walding contested the resulting 1967 by-election against four others: Gordon Cruden, John O'Brien, Goldingham and P. J. Wedderspoon. Walding represented the Palmerston North electorate from 1967 to 1975, when he was defeated by John Lithgow, from 1978 to 1981. Between 1972 and 1974, he was Minister of Overseas Trade, Minister for the Environment, Minister of Recreation and Sport. Six months prior to the 1981 election, he announced his retirement from Parliament. In late 1984, he was appointed High Commissioner to the United Kingdom. Three months after starting the position, he died on 5 June 1985 in London. Walding's wife, Eileen Walding, was appointed a Companion of the Queen's Service Order for community service in the 1990 New Year Honours, she died in Havelock North on 8 June 2017.

Wilson, James Oakley. New Zealand Parliamentary Record, 1840–1984. Wellington: V. R. Ward, Govt. Printer. OCLC 154283103

The Economic Freedom Fighters is a South African far-left Pan-Africanist political party. It was founded by expelled former African National Congress Youth League President Julius Malema, his allies, in 2013. Malema is President of the EFF, heading the Central Command Team which serves as the central structure of the party, it is the third-largest party in both houses of the South African Parliament. At a 26 July 2013 press briefing in Soweto, Malema announced that the new party had over 1000 members, double the 500 required for registration with the Independent Electoral Commission; the EFF is now registered with the IEC, after an objection to its registration by the Freedom Front Plus was dismissed in September 2013. In 2015, the EFF suspended MP Lucky Twala and expelled three MPs, Mpho Ramakatsa, Andile Mngxitama and Khanyisile Litchfield-Tshabalala. Mngxitama formed his own party, named Black First Land First, while Litchfield-Tshabalala joined the United Democratic Movement. Malema has been chiefly accused by former members of purging his critics to consolidate his power, thus ruling the party with an iron fist.

Malema acknowledged this criticism in a press conference and further went on to say, the party should have expelled more ill disciplined members. The EFF "draws inspiration from the broad Marxist–Leninist tradition and Fanonian schools of thought in their analyses of the state, imperialism and class contradictions in every society", according to one of its declarations, it criticises the African National Congress and their primary opposition, the Democratic Alliance, for their pro-business stances, which it claims have sold out the black people of South Africa to capitalism as cheap labour. It promises to tackle corruption, provide quality social housing, provide free primary healthcare and education for all, as well as proposing to expropriate stolen land, nationalise the mining and banking sectors, double welfare grants and the minimum wage, end the proposed toll system for highways; the EFF takes significant inspiration from Thomas Sankara in terms of both ideology. In a May 2014 column, the prominent EFF member Jackie Shandu declared his party a "proudly Sankarist formation".

The EFF has been vocal in its criticism of black business owners and black owners of mining companies in South Africa. In an address at the Oxford Union in November 2015, Malema spoke out against billionaire mining company owner Patrice Motsepe. Further protests in 2015, the EFF delivered demands that included the socialization of the mining sector and called for more explicit targets for the 26% BEE ownership required by law; the EFF is a vocal proponent of expanding the role of South African state owned enterprises in the country's economy. Malema addressed a crowd in Marikana, Rustenburg in the platinum mining area, blaming mining companies and calling out platinum mining company Lonmin in particular, for poverty in the region; the party supports the re-introduction of the death penalty. In 2016, after local elections in South Africa, the EFF has suggested that they will back the Democratic Alliance in hung-metro areas, but would not be entering into a coalition with any political party in South Africa.

The EFF was the only parliamentary party. High-profile members of the Central Command Team include Floyd Shivambu, Fana Mokoena and Mbuyiseni Ndlozi. Controversial businessman Kenny Kunene joined the Central Command Team in July 2013 before resigning from the Central Command Team on 20 August 2013 and from the organisation on 26 August 2013. On 4 November 2013, it was announced that Dali Mpofu had left the African National Congress after 33 years of membership and joined the EFF. Musician and actress Ntando Duma publicly pledged allegiance to EFF in February 2019. According to a November 2013 Ipsos survey, the party's supporters are younger than average, with 49% being younger than 24, overwhelmingly black and male, with women representing only 33% of the support base. A disproportionate number of supporters live in Malema's home province of Limpopo, while only 1% live in KwaZulu-Natal, a more populous province. A 2018 survey conducted by social research company Citizen Surveys found that around 70% of EFF supporters were between the ages of 18 - 34, overwhelmingly black based in major metropolitan cities, predominantly male with 43% of their support base located in Gauteng Province.

The party was expected to make an impact in the 2014 general election, taking between 4 per cent and 8 per cent of the national vote. This was enough for the party to hold the balance of power in provinces where the governing African National Congress was in danger of losing its absolute majority; the ANC retained whilst the EFF got 6.35 % of the vote in the 2014 election. On 6 August 2015 the EFF announced that it has secured a Constitutional court case for its Jacob Zuma campaign of "#PayBackTheMoney"; the case was heard on the 9 February 2016. The Judgement was released by Chief Justice Mogoeng Mogoeng; the judgement stated that The President has violated the Constitution of South Africa, along with the Speaker of the National Assembly Baleka Mbete. The President was given 60 days to fulfill the requirements of the Public Protector Thuli Madonsela. On 27 February 2018 the EFF tabled a motion in The National Assembly to amend the Constitution so as to allow for the expropriation of land without compensation.

The motion, brought by the EFF leader Julius Malema, was adopted with a vote of 241 in support, 83 against. The only parties who did not support the motion were the Democratic Alliance, Freedom Front Plus and the ACDP. Land Expropriation is one of the EFF's Seven cardin

Club Gimnàstic de Tarragona referred to as Nàstic, is a Spanish sports club based in Tarragona, in the autonomous community of Catalonia. Its football team plays in Segunda División B – Group 3; the club is one of the oldest football clubs in Spain. It has teams competing in athletics, tennis, table tennis and futsal, but a football team was not formed until 1914; the team enjoyed a three-year La Liga spell in its beginnings. Since 1972, the team has played home games at Nou Estadi; the club was founded on 1 March 1886 by a group of fifteen people who met at the Cafè del Centre on Rambla Nova. The majority of the club's early members belonged to the upper middle class and, as the club name suggests, was founded to promote gymnastics; the club members began to organise fencing, hiking and cycling. In 1914, the club absorbed a local football club called the Club Olímpic de Tarragona and formed its own football team using the former colours of Olímpic: red and black. In those days the team played. In January 1918, Gimnàstic made its debut as a football team in the Campionat de Catalunya and by 1927 were crowned champions in the second division.

In the 1943–44 season the team appeared in the Tercera División and in the following season moved up to the Segunda División. In the 1946 -- 47 season Nàstic entered the La Liga. In 1947 it reached the Copa del Generalísimo semi-final but lost to the RCD Espanyol, having beaten the FC Barcelona in the previous round; the team finished its debut first division season in seventh place, with the highlight of the season coming on 11 January 1948 with a 3–1 win against the Real Madrid at the Bernabéu, thus becoming the first team to do so. The club played two further seasons in the top level, being relegated in 1949–50 after losing a play-off to the CD Alcoyano; the team moved to the new Nou Estadi in 1972. Fifty-six years for the 2006–07 season, Gimnàstic returned to the top flight. Along with coach Luis César Sampedro, some of the players responsible for the promotion included veterans Antonio Pinilla and Albano Bizarri. Rubén Castro, Ariza Makukula and Javier Portillo were brought in; the club was placed in the relegation zone for 33 of the 38 rounds dropping down a division.

Sampedro was replaced mid-season by Paco Flores. In the middle of 2007 the club was crowned the Copa Catalunya champions after a 2–1 win over the FC Barcelona, with goals from Pinilla and Tati Maldonado. After returning to the second level Gimnàstic achieved a mid-table position in 2007–08 and 2008–09 with César Ferrando in charge of the team. However, in the 2009–10 and 2010–11 seasons, the club only managed to rank one position above the relegation zone. In the 2011–12 campaign the team was relegated to the Segunda División B after only winning six games out of 42. On 12 September 2012 Nàstic won the second Catalan Cup in its history, after defeating the AEC Manlleu with an Eugeni goal. In the 2014–15 campaign, after finishing first in its group, the club returned to the second level after defeating the SD Huesca in the play-offs. In the 2018–19 campaign the team was relegated to the Segunda División B ending a four-year run in the second division. There are two small ultras groups: a right-wing political group called Ultras Tarraco and an antifa group called Nàstic Crew.

4 seasons in La Liga 22 seasons in Segunda División 26 seasons in Segunda División B 25 seasons in Tercera División 3 seasons in Categorías Regionales The numbers are established according to the official website:www.gimnasticdetarragona.com and www.lfp.es As of 18 November 2019Note: Flags indicate national team as defined under FIFA eligibility rules. Players may hold more than one non-FIFA nationality. Note: Flags indicate national team as defined under FIFA eligibility rules. Players may hold more than one non-FIFA nationality. Players who appeared in more than 100 league matches for the club and/or reached international status. Most appearances - 528, Santi Coch Most goals - 181, Valero Serer Copa Catalunya: 2007–08, 2011–12, 2016–17 Segunda División B: 1996–97 Tercera División: 1944–45, 1954–55, 1960–61, 1965–66, 1966–67, 1971–72, 1977–78 Catalan Cup Second Division: 1926–27 Segunda División B League Cup: 1983–84 CF Pobla de Mafumet Kitchee SC C. D. Olimpia Fuerte San Francisco Ciutat de Tarragona Trophy Official website Futbolme team profile Soccerway.com team profile