Abelian subgroups of topological groups
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- by Siegfried K. Grosser and Wolfgang N. Herfort PDF
- Trans. Amer. Math. Soc. 283 (1984), 211-223 Request permission
Abstract:
In [1] Šmidt’s conjecture on the existence of an infinite abelian subgroup in any infinite group is settled by counterexample. The well-known Hall-Kulatilaka Theorem asserts the existence of an infinite abelian subgroup in any infinite locally finite group. This paper discusses a topological analogue of the problem. The simultaneous consideration of a stronger condition—that centralizers of nontrivial elements be compact—turns out to be useful and, in essence, inevitable. Thus two compactness conditions that give rise to a profinite arithmetization of topological groups are added to the classical list (see, e.g., [13 or 4]).References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 283 (1984), 211-223
- MSC: Primary 22A05; Secondary 22D05
- DOI: https://doi.org/10.1090/S0002-9947-1984-0735417-4
- MathSciNet review: 735417