classification of semisimple groups

For every semisimple group G there is a normal subgroupMathworldPlanetmath H of G, (called the centerless competely reducible radicalPlanetmathPlanetmathPlanetmathPlanetmath) which isomorphicPlanetmathPlanetmathPlanetmath to a direct productMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath of nonabelianPlanetmathPlanetmathPlanetmath simple groupsMathworldPlanetmathPlanetmath such that conjugationMathworldPlanetmath on H gives an injection into Aut(H). Thus G is isomorphic to a subgroupMathworldPlanetmathPlanetmath of Aut(H) containing the inner automorphisms, and for every group H isomorphic to a direct product of non-abelianMathworldPlanetmath simple groups, every such subgroup is semisimplePlanetmathPlanetmathPlanetmath.

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