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This article is cited in 5 scientific papers (total in 5 papers)
Two Criteria for Nonsimplicity of a Group Possessing a Strongly Embedded Subgroup and a Finite Involution
A. I. Sozutov
Abstract:
A proper subgroup $H$ of a group $G$ is said to be strongly embedded if $2\in\pi (H)$ and $2\notin\pi(H\cap H^g)$ ($\forall g\in G\setminus H$). An involution $i$ of $G$ is said to be finite if $|ii^g|<\infty$ ($\forall g\in G$). As is known, the structure of a (locally) finite group possessing a strongly embedded subgroup is determined by the theorems of Burnside and Brauer–Suzuki, provided that the Sylow 2-subgroup contains a unique involution. In this paper, sufficient conditions for the equality $m_2(G)=1$ are established, and two analogs of the Burnside and Brauer–Suzuki theorems for infinite groups $G$ possessing a strongly embedded subgroup and a finite involution are given.
Received: 24.03.2000
Citation:
A. I. Sozutov, “Two Criteria for Nonsimplicity of a Group Possessing a Strongly Embedded Subgroup and a Finite Involution”, Mat. Zametki, 69:3 (2001), 443–453; Math. Notes, 69:3 (2001), 401–410
Linking options:
https://www.mathnet.ru/eng/mzm516https://doi.org/10.4213/mzm516 https://www.mathnet.ru/eng/mzm/v69/i3/p443
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