The formation of finite groups with a supersolvable π-hall subgroup

Autor:	Xiaolan Yi, L. A. Shemetkov
Rok vydání:	2010
Předmět:	p-group Combinatorics Hall subgroup Normal subgroup Complement (group theory) Subgroup General Mathematics Index of a subgroup Characteristic subgroup Fitting subgroup Mathematics
Zdroj:	Mathematical Notes. 87:258-263
ISSN:	1573-8876 0001-4346
DOI:	10.1134/s0001434610010323
Popis:	Let G be a finite group having a π-subgroup H such that |G: H| is not divisible by the numbers in π. In this case, the subgroup H is referred to as a π-Hall subgroup, and the group G by itself is referred to as a Eπ-group. If, moreover, the group H is supersolvable, then G is referred to as an Eπu-group. It is proved in the paper that the class of all Eπu-groups is a solvably saturated formation, and the proof is carried out without using the classification of finite groups.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::517bf7f31303a73f688b3e9bcda37b8c https://doi.org/10.1134/s0001434610010323 Zobrazit plný text záznamu Plný text ve formátu PDF