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

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

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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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
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