# classification of semisimple groups

For every semisimple group $G$ there is a normal subgroup $H$ of $G$, (called the centerless competely reducible radical) which isomorphic to a direct product of nonabelian simple groups such that conjugation on $H$ gives an injection into $\mathrm{Aut}\,(H)$. Thus $G$ is isomorphic to a subgroup of $\mathrm{Aut}\,(H)$ containing the inner automorphisms, and for every group $H$ isomorphic to a direct product of non-abelian simple groups, every such subgroup is semisimple.

Title classification of semisimple groups ClassificationOfSemisimpleGroups 2013-03-22 13:17:10 2013-03-22 13:17:10 bwebste (988) bwebste (988) 4 bwebste (988) Definition msc 20D05