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Automorphism group of a group

1 byte added, 00:51, 25 February 2014
Particular groups
| [[cyclic group:Z7]] || 7 || [[cyclic group:Z6]] || 6 || [[endomorphism structure of cyclic group:Z7]] || In particular, for a prime <math>p</math>, the automorphism group of the cyclic group of order <math>p</math> is the cyclic group of order <math>p - 1</math>.
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| [[cyclic group:Z8]] || 8 || [[cyclic Klein four-group:Z4]] || 4 || [[endomorphism structure of cyclic group:Z8]] || For a [[finite cyclic group]] of order <math>n</math>, the automorphism group is of order <math>\varphi(n)</math> where <math>\varphi</math> denotes the [[Euler totient function]]. Further, the automorphism group is cyclic iff <math>n</math> is 2,4, a power of an odd prime, or twice a power of an odd prime.
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| [[direct product of Z4 and Z2]] || 8 || [[dihedral group:D8]] || 8 || [[endomorphism structure of direct product of Z4 and Z2]] ||
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