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Mat. Zametki, 2001, Volume 69, Issue 3, Pages 443–453 (Mi mz516)  

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.

DOI: https://doi.org/10.4213/mzm516

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English version:
Mathematical Notes, 2001, 69:3, 401–410

Bibliographic databases:

UDC: 512.544
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

Citation in format AMSBIB
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\paper Two Criteria for Nonsimplicity of a Group Possessing a Strongly Embedded Subgroup and a Finite Involution
\jour Mat. Zametki
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\issue 3
\pages 443--453
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\crossref{https://doi.org/10.4213/mzm516}
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\zmath{https://zbmath.org/?q=an:0998.20027}
\transl
\jour Math. Notes
\yr 2001
\vol 69
\issue 3
\pages 401--410
\crossref{https://doi.org/10.1023/A:1010291610395}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Sozutov, A. K. Shlepkin, “On Some Groups with Finite Involution Saturated with Finite Simple Groups”, Math. Notes, 72:3 (2002), 398–410  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. I. Senashov, A. I. Sozutov, V. P. Shunkov, “Investigation of groups with finiteness conditions in Krasnoyarsk”, Russian Math. Surveys, 60:5 (2005), 805–848  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. V. I. Senashov, “On Shunkov Groups with a strongly embedded subgroup”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S210–S217  mathnet  crossref  isi  elib
    4. V. I. Senashov, “O gruppakh Shunkova s silno vlozhennoi pochti sloino konechnoi podgruppoi”, Tr. IMM UrO RAN, 16, no. 3, 2010, 234–239  mathnet  elib
    5. Senashov V.I., “On Groups with a Strongly Imbedded Subgroup Having an Almost Layer-Finite Periodic Part”, Ukr. Math. J., 64:3 (2012), 433–440  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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