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Algebra i logika, 2012, Volume 51, Number 3, Pages 321–330 (Mi al537)  
This article is cited in 2 scientific papers (total in 2 papers)

Groups with given properties of finite subgroups

D. V. Lytkinaab, V. D. Mazurovca

a Novosibirsk State University, Novosibirsk, Russia
b Siberian State University of Telecommunications and Information Sciences, Novosibirsk, Russia
c Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
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Abstract: Suppose that in every finite even order subgroup $F$ of a periodic group $G$, the equality $[u,x]^2=1$ holds for any involution $u$ of $F$ and for an arbitrary element $x$ of $F$. Then the subgroup $I$ generated by all involutions in $G$ is locally finite and is a $2$-group. In addition, the normal closure of every subgroup of order $2$ in $G$ is commutative.
Keywords: periodic group, finite group, locally finite group, involution.
Received: 13.02.2012
English version:
Algebra and Logic, 2012, Volume 51, Issue 3, Pages 213–219
DOI: https://doi.org/10.1007/s10469-012-9184-7
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: D. V. Lytkina, V. D. Mazurov, “Groups with given properties of finite subgroups”, Algebra Logika, 51:3 (2012), 321–330; Algebra and Logic, 51:3 (2012), 213–219
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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