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Mat. Sb. (N.S.), 1977, Volume 102(144), Number 2, Pages 248–259 (Mi msb2681)  

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

The connected component of the group of automorphisms of a locally compact group

O. V. Mel'nikov


Abstract: The paper is devoted to the investigation of the group of automorphisms $\operatorname{Aut}G$ of a locally compact group $G$. $\operatorname{Aut}G$ is equipped with a topology which is naturally related to the topology of $G$.
The connected component of $\operatorname{Aut}G$ is determined for a group $G$ which can be written as a semidirect product of a vector group and a group possessing an open compact subgroup.
For a central group $G$ an explicit representation of $(\operatorname{Aut}G)_0$ is obtained in the form of a product of certain well-defined subgroups of $\operatorname{Aut}G$.
The following result is obtained:
Theorem. {\it If $G$ is locally compact group whose connected component is compact, then the connected component of $\operatorname{Aut}G$ is also compact.}
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1977, 31:2, 219–229

Bibliographic databases:

UDC: 519.46
MSC: Primary 22D45; Secondary 18H10
Received: 05.03.1975

Citation: O. V. Mel'nikov, “The connected component of the group of automorphisms of a locally compact group”, Mat. Sb. (N.S.), 102(144):2 (1977), 248–259; Math. USSR-Sb., 31:2 (1977), 219–229

Citation in format AMSBIB
\Bibitem{Mel77}
\by O.~V.~Mel'nikov
\paper The connected component of the group of automorphisms of a~locally compact group
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 102(144)
\issue 2
\pages 248--259
\mathnet{http://mi.mathnet.ru/msb2681}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=447468}
\zmath{https://zbmath.org/?q=an:0349.22004|0386.22008}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 31
\issue 2
\pages 219--229
\crossref{https://doi.org/10.1070/SM1977v031n02ABEH002299}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1977FY72200006}


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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. Dieter Remus, Luchezar Stojanov, “Complete minimal and totally minimal groups”, Topology and its Applications, 42:1 (1991), 57  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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