most recent 30 from http://mathoverflow.net 2013-05-24T09:20:20Z http://mathoverflow.net/feeds/question/101145 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/101145/how-to-find-the-normalizer-of-a-finite-subroup-in-a-lie-group Gang Han 2012-07-02T14:06:08Z 2012-07-02T14:06:08Z

<p>If a group $G$ is generated by finitely many subgroups $G_i$ and $H$ a subgroup of $G$, under which conditions can $N_G(K)$, the normalizer of $K$ in $G$, be generated by all the normailizers $N_{G_i}(K)$?</p> <p>More concretely, let $G$ be a compact connected Lie group and $K$ a finite abelian subgroup of $G$ whose centralizer in $G$ is $K$, i.e., $K$ is a maximal finite abelian subgroup of $G$. Assume that $G$ is generated by closed connected abelian subgroups $G_i$, $i=1\cdots n$. (Each $G_i$ is a torus.) It is known that $K$ normailizes each $G_i$. Is $N_G(K)$, the normalizer of $K$ in $G$, generated by all the normailizers $N_{G_i}(K)$,$i=1\cdots n$ ?</p> <p>This is true for all the examples I know. But I cannot find a proof. Your help is very appreciated!</p>