Remarks on g-reversible topological groups

Our main objective is to study g-reversible groups introduced in Chatyrko and Shakhmatov (2020) [3]. We first give a necessary and sufficient condition for a locally compact group with an open compact subgroup to be g-reversible, it can be applied to give complete solutions of Questions 8.5, 9.7, 9....

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Bibliographic Details
Published in:Topology and its applications 2021-03, Vol.290, p.107583, Article 107583
Main Authors: He, Wei, Peng, Dekui
Format: Article
Language:English
Subjects:
Automorphisms
g-reversible groups
Locally compact groups
Pontryagin duality
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Summary:Our main objective is to study g-reversible groups introduced in Chatyrko and Shakhmatov (2020) [3]. We first give a necessary and sufficient condition for a locally compact group with an open compact subgroup to be g-reversible, it can be applied to give complete solutions of Questions 8.5, 9.7, 9.8, and Problem 9.6 in the previous article [3]. We also investigate g-reversibility of some precompact abelian groups, in particular, we give a pseudocompact g-reversible abelian group which is not minimal, which answers Question 11.5 in the same article [3] negatively. We give descriptions of connected (or totally disconnected) compact abelian groups of which all subgroups are g-reversible. Finally, we give a characterization of the abelian groups which admit hereditarily g-reversible compact group topologies.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2020.107583