classification of semisimple groups

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

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