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Almost simple group : ウィキペディア英語版 | Almost simple group In mathematics, a group is said to be almost simple if it contains a non-abelian simple group and is contained within the automorphism group of that simple group: if it fits between a (non-abelian) simple group and its automorphism group. In symbols, a group ''A'' is almost simple if there is a simple group ''S'' such that == Examples ==
* Trivially, nonabelian simple groups and the full group of automorphisms are almost simple, but proper examples exist, meaning almost simple groups that are neither simple nor the full automorphism group. * For or the symmetric group is the automorphism group of the simple alternating group so is almost simple in this trivial sense. * For there is a proper example, as sits properly between the simple and due to the exceptional outer automorphism of Two other groups, the Mathieu group and the projective general linear group also sit properly between and
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