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Mathematics of the USSR-Izvestiya, 1989, Volume 32, Issue 3, Pages 501–521
DOI: https://doi.org/10.1070/IM1989v032n03ABEH000778
(Mi im1192)
 

This article is cited in 2 scientific papers (total in 2 papers)

Finite automorphism groups of torsion-free Abelian groups of finite rank

S. F. Kozhukhov
References:
Abstract: Abelian torsion-free groups of finite rank with finite automorphism groups are considered as rigid extensions of a system of strongly indecomposable groups $A_j$, $j=1,\dots,k$, of finite rank and having finite automorphism groups, by a finite $p$-group $P$. Such groups are called $(A,p)$-groups. The author introduces for $(A,P)$-groups the concept of $(A,P)$-type, which represents a choice of $k$ integer matrices. A complete description of $(A,P)$-groups is given by means of $(A,P)$-types. Using this description, a series of problems on finite groups of automorphisms of torsion-free abelian groups of finite rank are solved. Furthermore, it is shown that the actual solution of any one of these problems comes down to a question of the consistency of a system of equations of the first degree modulo $p^t$, where $p^t$ is the maximal order of elements of $P$.
Bibliography: 11 titles.
Received: 03.05.1986
Bibliographic databases:
UDC: 512.541
MSC: 20K15, 20K30
Language: English
Original paper language: Russian
Citation: S. F. Kozhukhov, “Finite automorphism groups of torsion-free Abelian groups of finite rank”, Math. USSR-Izv., 32:3 (1989), 501–521
Citation in format AMSBIB
\Bibitem{Koz88}
\by S.~F.~Kozhukhov
\paper Finite automorphism groups of torsion-free Abelian groups of finite rank
\jour Math. USSR-Izv.
\yr 1989
\vol 32
\issue 3
\pages 501--521
\mathnet{http://mi.mathnet.ru//eng/im1192}
\crossref{https://doi.org/10.1070/IM1989v032n03ABEH000778}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=954294}
\zmath{https://zbmath.org/?q=an:0667.20047|0656.20062}
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  • https://doi.org/10.1070/IM1989v032n03ABEH000778
  • https://www.mathnet.ru/eng/im/v52/i3/p501
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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