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Matematicheskie Zametki, 2010, Volume 87, Issue 2, Pages 280–286
DOI: https://doi.org/10.4213/mzm7701
(Mi mzm7701)
 

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
Full-text PDF (454 kB) Citations (2)
References:
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
English version:
Mathematical Notes, 2010, Volume 87, Issue 2, Pages 258–263
DOI: https://doi.org/10.1134/S0001434610010323
Bibliographic databases:
UDC: 512.542.6
Language: Russian
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
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm7701
  • https://www.mathnet.ru/eng/mzm/v87/i2/p280
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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