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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$.


References [Enhancements On Off] (What's this?)

  • [1] K. Iwasawa, Topological groups with invariant compact neighborhoods of the identity, Ann. of Math. (2) 54 (1951), 345-348. MR 13, 206. MR 0043106 (13:206c)
  • [2] B. H. Neumann, Groups with finite classes of conjugate elements, Proc. London Math. Soc. (3) 1 (1951), 178-187. MR 13, 316. MR 0043779 (13:316c)

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Additional Information

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

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