# 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 |
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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 |