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Automorphism group of alternating group:A6

157 bytes added, 02:35, 2 November 2011
Definition
# It is the [[defining ingredient::automorphism group]] of [[defining ingredient::symmetric group:S6]].
Note that for any <math>n \ne 2,6</math>, the [[automorphism group]] of the alternating group <math>A_n</math> is precisely the symmetric group <math>S_n</math>, which is a [[complete group]]. The case <math>n = 2</math> is uninteresting, and the case <math>n = 6</math> is the only case where the automorphism group of the alternating group is strictly ''bigger'' than the symmetric group. Similarly, it is the only case where the automorphism group of the symmetric group is strictly ''bigger'' than the symmetric group. {{further|[[symmetric groups on finite sets are complete]]}}
==Arithmetic functions==
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