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Mat. Zametki, 1977, Volume 22, Issue 5, Pages 611–620 (Mi mz8085)  

Groups with a dense system of complemented nonextremal Abelian subgroups

N. S. Chernikov

Kiev State Univesity

Abstract: Suppose $G$ is a group containing nonextremal Abelian subgroups. We say that it possesses a dense system of complemented nonextremal Abelian subgroups if for any two nonextremal Abelian subgroups $A\subset B$ of $G$, the first of which is not maximal in the second, there exists a $G$-complemented subgroup contained strictly between them. In this paper we obtain a description of the locally finite groups with such a dense system of subgroups. In particular, all infinite Abelian subgroups of such groups are complemented.

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English version:
Mathematical Notes, 1977, 22:5, 834–838

Bibliographic databases:

UDC: 519.4
Received: 10.05.1976

Citation: N. S. Chernikov, “Groups with a dense system of complemented nonextremal Abelian subgroups”, Mat. Zametki, 22:5 (1977), 611–620; Math. Notes, 22:5 (1977), 834–838

Citation in format AMSBIB
\Bibitem{Che77}
\by N.~S.~Chernikov
\paper Groups with a~dense system of complemented nonextremal Abelian subgroups
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 5
\pages 611--620
\mathnet{http://mi.mathnet.ru/mz8085}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=480746}
\zmath{https://zbmath.org/?q=an:0383.20019}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 5
\pages 834--838
\crossref{https://doi.org/10.1007/BF01098345}


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