| Power Automorphism |
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| group theory | |
| group automorphisms | |
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Alternatively, power automorphisms are characterized as automorphisms that send each element of the group to some power of that element. This explains the choice of the term ''power''. The power automorphisms of a group form a subgroup of the whole Automorphism Group . This subgroup is denoted as where is the group. A universal power automorphism is a power automorphism where the power to which each element is raised is the same. For instance, each element may go to its cube. Here are some facts about the powering index:
The group of power automorphisms commutes with the group of Inner Automorphism s when viewed as subgroups of the automorphism group. Thus, in particular, power automorphisms that are also inner must arise as Conjugations by elements in the second group of the Upper Central Series . References |
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