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Sibirsk. Mat. Zh., 2012, Volume 53, Number 3, Pages 543–557 (Mi smj2344)  

This article is cited in 3 scientific papers (total in 3 papers)

On finite Alperin $2$-groups with elementary abelian second commutants

B. M. Veretennikov

Ural Federal University, Ekaterinburg

Abstract: By an Alperin group we mean a group in which the commutant of each $2$-generated subgroup is cyclic. Alperin proved that if $p$ is an odd prime then all finite p-groups with this property are metabelian. The today's actual problem is the construction of examples of nonmetabelian finite Alperin $2$-groups. Note that the author had given some examples of finite Alperin $2$-groups with second commutants isomorphic to $Z_2$ and $Z_4$ and proved the existence of finite Alperin $2$-groups with cyclic second commutants of however large order by appropriate examples. In this article the existence is proved of finite Alperin $2$-groups with abelian second commutants of however large rank.

Keywords: $2$-group, Alperin group, commutant (commutator subgroup), definition of a group by generators and defining relations.

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English version:
Siberian Mathematical Journal, 2012, 53:3, 431–443

Bibliographic databases:

UDC: 512.54
Received: 03.06.2010

Citation: B. M. Veretennikov, “On finite Alperin $2$-groups with elementary abelian second commutants”, Sibirsk. Mat. Zh., 53:3 (2012), 543–557; Siberian Math. J., 53:3 (2012), 431–443

Citation in format AMSBIB
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\paper On finite Alperin $2$-groups with elementary abelian second commutants
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 3
\pages 543--557
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\jour Siberian Math. J.
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\pages 431--443
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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. B. M. Veretennikov, “On the second commutants of finite Alperin groups”, Siberian Math. J., 55:1 (2014), 19–34  mathnet  crossref  mathscinet  isi
    2. Wilkens B., “on the Derived Length of a Finite Alperin 2-Group”, J. Group Theory, 17:1 (2014), 151–174  crossref  mathscinet  zmath  isi  elib  scopus
    3. B. M. Veretennikov, “O beskonechnykh gruppakh Alperina”, Sib. elektron. matem. izv., 12 (2015), 210–222  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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