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
Canonical name	ClassificationOfSemisimpleGroups
Date of creation	2013-03-22 13:17:10
Last modified on	2013-03-22 13:17:10
Owner	bwebste (988)
Last modified by	bwebste (988)
Numerical id	4
Author	bwebste (988)
Entry type	Definition
Classification	msc 20D05