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Ascendant subgroup information


In mathematics, in the field of group theory, a subgroup of a group is said to be ascendant if there is an ascending series starting from the subgroup and ending at the group, such that every term in the series is a normal subgroup of its successor.

The series may be infinite. If the series is finite, then the subgroup is subnormal. Here are some properties of ascendant subgroups:

  • Every subnormal subgroup is ascendant; every ascendant subgroup is serial.
  • In a finite group, the properties of being ascendant and subnormal are equivalent.
  • An arbitrary intersection of ascendant subgroups is ascendant.
  • Given any subgroup, there is a minimal ascendant subgroup containing it.

and 22 Related for: Ascendant subgroup information

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Ascendant subgroup

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field of group theory, a subgroup of a group is said to be ascendant if there is an ascending series starting from the subgroup and ending at the group...

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Normal subgroup

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Contranormal subgroup Abnormal subgroup Self-normalizing subgroup Characteristic subgroup Fully characteristic subgroup Subnormal subgroup Ascendant subgroup Descendant...

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Subnormal subgroup

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subgroup of G is normal in G, then G is called a T-group. Characteristic subgroup Normal core Normal closure Ascendant subgroup Descendant subgroup Serial...

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Quasinormal subgroup

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quasinormal subgroup is ascendant. A conjugate permutable subgroup is one that commutes with all its conjugate subgroups. Every quasinormal subgroup is conjugate...

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Serial subgroup

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subnormal subgroup of G. Then every subnormal subgroup of G is serial. If the chain C is well-ordered and ascending, then H is an ascendant subgroup of G;...

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Descendant subgroup

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a normal subgroup of its predecessor. The series may be infinite. If the series is finite, then the subgroup is subnormal. Ascendant subgroup Martyn R...

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Glossary of group theory

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hold for any pair g, h ∈ G. ascendant subgroup A subgroup H of a group G is ascendant if there is an ascending subgroup series starting from H and ending...

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Strictly simple group

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no proper nontrivial ascendant subgroups. That is, G {\displaystyle G} is a strictly simple group if the only ascendant subgroups of G {\displaystyle G}...

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Absolutely simple group

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simple. The property of being strictly simple is somewhere in between. Ascendant subgroup Strictly simple group Robinson, Derek J. S. (1996), A course in the...

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Qahtanite

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back to Sem, son of Noah, but only Adnanites can claim Abraham as their ascendant, and the lineage of Mohammed, the Seal of Prophets (khatim al-anbiya')...

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Indigenous peoples of the Americas

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households where the head of the household, his or her spouse or any of their ascendants claimed to speak an Indigenous language. "Censo de Población y Vivienda...

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History of the Yoruba people

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Yoruba who had rallied in defense under the military leadership of the ascendant Ibadan clan, which rose from the old Oyo Empire, and of the Ijebu city-states...

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Sovereign citizen movement

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ISBN 978-1-4408-3095-2. Hodge, Edwin (November 26, 2019). "The Sovereign Ascendant: Financial Collapse, Status Anxiety, and the Rebirth of the Sovereign...

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Pirzada

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and the suffix zada means; son of. It also serves as surname for their ascendants in many Indo-Aryan cultures and their accompanying languages, with Pirzada...

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English Reformation

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eroded and discredited". In 1546, the conservatives were once again in the ascendant. A series of controversial sermons preached by the Protestant Edward Crome...

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Somali Civil War

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the ARPCT, a coalition of U.S.-backed militia leaders, confronted the ascendant Islamic Courts Union (ICU). However, the ICU won a decisive victory in...

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Second Congo War

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2016. Retrieved 16 February 2016. Vick, Karl (23 January 2001). "The Ascendant Son in Congo". The Washington Post. ISSN 0190-8286. Archived from the...

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Tokelauan language

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be-soon COMP sit DIR DET star DEM 'Very soon that star will be in the ascendant.' The Tokelauan language also must take into mind the systematics of its...

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Jutes

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replace him as ruler of Kent. In the 680s, the Kingdom of Wessex was in the ascendant, the alliance between the South Saxons and the Mercians and their control...

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British Jamaicans

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19 March 2022. Velasco, Matthew (9 February 2022). "Mahalia: Hip-Pop's Ascendant Star". V. Retrieved 19 March 2022. Wurzer, Cathy (28 February 2019). "Grammy...

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Wellesley Tudor Pole

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inaugurated the Church of the New Age, a church in which woman was in the ascendant and Bride, the Celtic embodiment of the Universal Feminine, was restored...

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Bifrenaria

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are epiphyte and the only Bifrenaria species with elongated rhizome and ascendant growth. Bifrenaria are comparatively easy to grow orchids. They should...

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