Curve Selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups

Details Curve Selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups Curve Selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups

2005-06-09

arxiv.org/abs/math/0506160v4

Mathematics

Group Theory

6 pages

Scientific paper

Using a strong version of the Curve Selection Lemma for real semianalytic sets, we prove that for an arbitrary connected Lie group $G$, each connected component of the set $E_n(G)$ of all elements of order $n$ in $G$ is a conjugacy class in $G$. In particular, all conjugacy classes of finite order in $G$ are closed. Some properties of connected components of $E_n(G)$ are also given.

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