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

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

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
\Bibitem{Soz01} \by A.~I.~Sozutov \paper Two Criteria for Nonsimplicity of a Group Possessing a Strongly Embedded Subgroup and a Finite Involution \jour Mat. Zametki \yr 2001 \vol 69 \issue 3 \pages 443--453 \mathnet{http://mi.mathnet.ru/mz516} \crossref{https://doi.org/10.4213/mzm516} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1846841} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000169324200012} 

• http://mi.mathnet.ru/eng/mz516
• https://doi.org/10.4213/mzm516
• http://mi.mathnet.ru/eng/mz/v69/i3/p443

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
3. V. I. Senashov, “On Shunkov Groups with a strongly embedded subgroup”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S210–S217
4. V. I. Senashov, “O gruppakh Shunkova s silno vlozhennoi pochti sloino konechnoi podgruppoi”, Tr. IMM UrO RAN, 16, no. 3, 2010, 234–239
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
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