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
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...
subgroup of G is normal in G, then G is called a T-group. Characteristic subgroup Normal core Normal closure Ascendantsubgroup Descendant subgroup Serial...
quasinormal subgroup is ascendant. A conjugate permutable subgroup is one that commutes with all its conjugate subgroups. Every quasinormal subgroup is conjugate...
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 ascendantsubgroup of G;...
a normal subgroup of its predecessor. The series may be infinite. If the series is finite, then the subgroup is subnormal. Ascendantsubgroup Martyn R...
hold for any pair g, h ∈ G. ascendantsubgroup A subgroup H of a group G is ascendant if there is an ascending subgroup series starting from H and ending...
no proper nontrivial ascendantsubgroups. That is, G {\displaystyle G} is a strictly simple group if the only ascendantsubgroups of G {\displaystyle G}...
simple. The property of being strictly simple is somewhere in between. Ascendantsubgroup Strictly simple group Robinson, Derek J. S. (1996), A course in the...
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')...
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...
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...
ISBN 978-1-4408-3095-2. Hodge, Edwin (November 26, 2019). "The Sovereign Ascendant: Financial Collapse, Status Anxiety, and the Rebirth of the Sovereign...
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...
eroded and discredited". In 1546, the conservatives were once again in the ascendant. A series of controversial sermons preached by the Protestant Edward Crome...
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...
2016. Retrieved 16 February 2016. Vick, Karl (23 January 2001). "The Ascendant Son in Congo". The Washington Post. ISSN 0190-8286. Archived from the...
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...
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...
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...
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...
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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