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Proceedings of the American Mathematical Society

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

 

 

A note on groups with relatively compact conjugacy classes


Author: Theodore W. Wilcox
Journal: Proc. Amer. Math. Soc. 42 (1974), 326-329
MSC: Primary 22D05
DOI: https://doi.org/10.1090/S0002-9939-1974-0330348-5
MathSciNet review: 0330348
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Abstract: In a more general form, the following structure theorem is proved. Let G be a locally compact group with small invariant neighborhoods. Then G has relatively compact conjugacy classes if and only if G is a direct product of a vector group V and a group L where L has a compact open normal subgroup K such that L/K has finite conjugacy classes.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0330348-5
Keywords: Locally compact group, splitting theorem, relatively compact conjugacy class, small invariant neighborhoods
Article copyright: © Copyright 1974 American Mathematical Society