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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 S \leq A \leq \operatorname(S).
== 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 n=5 or n \geq 7, the symmetric group S_n is the automorphism group of the simple alternating group A_n, so S_n is almost simple in this trivial sense.
* For n=6 there is a proper example, as S_6 sits properly between the simple A_6 and \operatorname(A_6), due to the exceptional outer automorphism of A_6. Two other groups, the Mathieu group M_ and the projective general linear group \operatorname_2(9) also sit properly between A_6 and \operatorname(A_6).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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