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Algebra Logika, 2015, Volume 54, Number 2, Pages 158–162 (Mi al685)  

This article is cited in 1 scientific paper (total in 1 paper)

The structure of groups possessing Carter subgroups of odd order

E. P. Vdovinab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: Let a group $G$ contain a Carter subgroup of odd order. It is shown that every composition factor of $G$ either is Abelian or is isomorphic to $L_2(3^{2n+1})$, $n\ge1$. Moreover, if $3$ does not divide the order of a Carter subgroup, then $G$ solvable.

Keywords: group, Carter subgroup of odd order, composition factor of group, solvable group.

DOI: https://doi.org/10.17377/alglog.2015.54.202

Full text: PDF file (110 kB)
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English version:
Algebra and Logic, 2015, 54:2, 105–107

Bibliographic databases:

UDC: 512.542
Received: 20.02.2015

Citation: E. P. Vdovin, “The structure of groups possessing Carter subgroups of odd order”, Algebra Logika, 54:2 (2015), 158–162; Algebra and Logic, 54:2 (2015), 105–107

Citation in format AMSBIB
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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. S. Vasilev, “Normalizatory silovskikh podgrupp v lineinykh i unitarnykh konechnykh gruppakh”, Algebra i logika, 59:1 (2020), 3–26  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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