Talk:Power automorphism
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"If the group is abelian, any powering index works." This statement must be restricted to finite groups, or be otherwise refined. In the group of all integers (with addition) only powering index 1 and -1 work. In the group that consists of all rationals whose denominator is a power of a prime $p$ (with addition) every nonzero integer is a valid powering index.
Maybe it should also made clearer that for finite abelian groups the "relatively prime" requirement still holds, disqualifying the word "any". I am not entirely sure if this is also necessary for infinite groups: in the Pruefer p-group the p-th power map seems to be a valid automorphism.
Leen Droogendijk (talk) 10:35, 13 February 2018 (UTC)
Endomorphism vs automorphism
[edit]The definition stated here, of mapping every subgroup into itself, is called a power endomorphism by Cooper (1968), who restricts the term power automorphism to automorphisms that map every subgroup onto itself. For instance the example of doubling the additive rationals given here is described by Cooper as an example of a power endomorphism that is not a power automorphism. Has the terminology shifted since then?
Cooper, Christopher D. H. (1968), "Power automorphisms of a group", Mathematische Zeitschrift, 107: 335–356, doi:10.1007/BF01110066, MR 0236253