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 | References | Similar Articles | Additional Information
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 $G$.
- Kenkichi Iwasawa, Topological groups with invariant compact neighborhoods of the identity, Ann. of Math. (2) 54 (1951), 345–348. MR 43106, DOI https://doi.org/10.2307/1969536
- B. H. Neumann, Groups with finite classes of conjugate elements, Proc. London Math. Soc. (3) 1 (1951), 178–187. MR 43779, DOI https://doi.org/10.1112/plms/s3-1.1.178
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Keywords:
Locally compact groups,
0-dimensional groups,
torsion elements
Article copyright:
© Copyright 1970
American Mathematical Society