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Mathematics of the USSR-Sbornik, 1977, Volume 31, Issue 2, Pages 219–229
DOI: https://doi.org/10.1070/SM1977v031n02ABEH002299
(Mi sm2681)
 

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
References:
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.
Received: 05.03.1975
Bibliographic databases:
UDC: 519.46
MSC: Primary 22D45; Secondary 18H10
Language: English
Original paper language: Russian
Citation: O. V. Mel'nikov, “The connected component of the group of automorphisms of a locally compact group”, 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 Math. USSR-Sb.
\yr 1977
\vol 31
\issue 2
\pages 219--229
\mathnet{http://mi.mathnet.ru//eng/sm2681}
\crossref{https://doi.org/10.1070/SM1977v031n02ABEH002299}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=447468}
\zmath{https://zbmath.org/?q=an:0349.22004|0386.22008}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1977FY72200006}
Linking options:
  • https://www.mathnet.ru/eng/sm2681
  • https://doi.org/10.1070/SM1977v031n02ABEH002299
  • https://www.mathnet.ru/eng/sm/v144/i2/p248
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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