On centralizers of generalized uniform subgroups of locally compact groups
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- by Kwan-Yuk Law Sit PDF
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Abstract:
Let $G$ be a locally compact group and $H$ a closed subgroup of $G$ such that the homogeneous space $G/H$ admits a finite invariant measure. Let ${Z_G}(H)$ be the centralizer of $H$ in $G$. It is shown that if $G$ is connected then ${Z_G}(H)$ modulo its center is compact. If $G$ is only assumed to be locally connected it is shown that the commutator subgroup of ${Z_G}(H)$ has compact closure. Consequences of these results are found for special classes of groups, such as Lie groups. An example of a totally disconnected group $G$ is given to show that the results for ${Z_G}(H)$ need not hold if $G$ is not connected or locally connected.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 201 (1975), 133-146
- MSC: Primary 22D05
- DOI: https://doi.org/10.1090/S0002-9947-1975-0354923-2
- MathSciNet review: 0354923