On bounded elements of linear algebraic groups
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- by Kwan-Yuk Claire Sit
- Trans. Amer. Math. Soc. 209 (1975), 185-198
- DOI: https://doi.org/10.1090/S0002-9947-1975-0379750-1
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Abstract:
Let $F$ be a local field of characteristic zero and ${\text {G }}$ a connected algebraic group defined over $F$. Let $G$ be the locally compact group of $F$-rational points. One characterizes the group $B(G)$ of $g \in G$ whose conjugacy class is relatively compact. For instance, if ${\text {G}}$ is $F$-split or reductive without anisotropic factors then $B(G)$ is the center of $G$. If $H$ is a closed subgroup of $G$ such that $G/H$ has finite volume, then the centralizer of $H$ in $G$ is contained in $B(G)$. If, moreover, $H$ is the centralizer of some $x \in G$ then $G/H$ is compact.References
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Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 209 (1975), 185-198
- MSC: Primary 22E20; Secondary 20G25
- DOI: https://doi.org/10.1090/S0002-9947-1975-0379750-1
- MathSciNet review: 0379750