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This article is cited in 2 scientific papers (total in 2 papers)
The Formation of Finite Groups with a Supersolvable $\pi$-Hall Subgroup
Yi Xiaolana, L. A. Shemetkovb a Zhejiang University
b Francisk Skaryna Gomel State University
Abstract:
Let $G$ be a finite group having a $\pi$-subgroup $H$ such that $|G:H|$ is not divisible by the numbers in $\pi$. In this case, the subgroup $H$ is referred to as a $\pi$-Hall subgroup, and the group $G$ by itself is referred to as a $E_\pi$-group. If, moreover, the group $H$ is supersolvable, then $G$ is referred to as an $E_\pi^u$-group. It is proved in the paper that the class of all $E_\pi^u$-groups is a solvably saturated formation, and the proof is carried out without using the classification of finite groups.
Keywords:
Hall subgroup, supersolvable group, formation, classification of finite groups, saturated formation, Frattini subgroup, monolithic group, subdirect product.
Received: 05.05.2009 Revised: 19.06.2009
Citation:
Yi Xiaolan, L. A. Shemetkov, “The Formation of Finite Groups with a Supersolvable $\pi$-Hall Subgroup”, Mat. Zametki, 87:2 (2010), 280–286; Math. Notes, 87:2 (2010), 258–263
Linking options:
https://www.mathnet.ru/eng/mzm7701https://doi.org/10.4213/mzm7701 https://www.mathnet.ru/eng/mzm/v87/i2/p280
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Abstract page: | 494 | Full-text PDF : | 196 | References: | 74 | First page: | 11 |
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