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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On existence of compact open normal subgroups of 0-dimensional groups


Authors: D. H. Lee and T. S. Wu
Journal: Proc. Amer. Math. Soc. 26 (1970), 526-528
MSC: Primary 22.20
DOI: https://doi.org/10.1090/S0002-9939-1970-0268325-1
MathSciNet review: 0268325
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Abstract: Let $ G$ be a locally compact 0-dimensional group, and let $ B(G)$ denote the set of all elements of $ G$ whose conjugacy classes are relatively compact. We proved that the group $ G$ has an open compact normal subgroup if and only if $ B(G)$ is open in $ G$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0268325-1
Keywords: Locally compact groups, 0-dimensional groups, torsion elements
Article copyright: © Copyright 1970 American Mathematical Society