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Mat. Zametki, 1976, Volume 19, Issue 5, Pages 735–743 (Mi mz7794)  

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

Compactness conditions for groups of automorphisms of topological groups

O. V. Mel'nikov

Institute of Mathematics, Academy of Sciences Byelorussian SSR

Abstract: It is proved that if $G$ is a compact, totally disconnected Abelian group and $\operatorname{Aut}G$ is its group of topological automorphisms (with the natural topology), then the following conditions are equivalent: (a) $\operatorname{Aut}G$ is compact; (b) $\operatorname{Aut}G$ is locally compact; (c) $\operatorname{Aut}G$ has small invariant neighborhoods of the identity; (d) $\operatorname{Aut}G$ is an $\overline{FC}$-group; (e) the factor group of $\operatorname{Aut}G$ by its center is compact; (f) the closure of the commutator subgroup of $\operatorname{Aut}G$ is compact; (g) $G\cong\Pi_p(F_p\oplus\Pi_{i=1}^{n_p}Z_p)$, where $F_p$ is a finite $p$-group, $Z_p$ is the additive group of $p$-adic integers, and $n_p<\infty$.

Full text: PDF file (734 kB)

English version:
Mathematical Notes, 1976, 19:5, 437–442

Bibliographic databases:

UDC: 519.4
Received: 07.10.1974

Citation: O. V. Mel'nikov, “Compactness conditions for groups of automorphisms of topological groups”, Mat. Zametki, 19:5 (1976), 735–743; Math. Notes, 19:5 (1976), 437–442

Citation in format AMSBIB
\Bibitem{Mel76}
\by O.~V.~Mel'nikov
\paper Compactness conditions for groups of automorphisms of topological groups
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 5
\pages 735--743
\mathnet{http://mi.mathnet.ru/mz7794}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=425000}
\zmath{https://zbmath.org/?q=an:0348.22004|0344.22006}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 5
\pages 437--442
\crossref{https://doi.org/10.1007/BF01142567}


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    This publication is cited in the following articles:
    1. Valeriu Popa, “On LCA groups with locally compact rings of continuous endomorphisms. I”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 3, 65–79  mathnet
  • Математические заметки Mathematical Notes
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