Abstract
An automorphism α of a group G is called a commuting automorphism if each element x in G commutes with its image α(x) under α. Let A(G) denote the set of all commuting automorphisms of G. Rai [Proc. Japan Acad., Ser. A 91 (5), 57–60 (2015)] has given some sufficient conditions on a finite p-group G such that A(G) is a subgroup of Aut(G) and, as a consequence, has proved that, in a finite p-group G of co-class 2, where p is an odd prime, A(G) is a subgroup of Aut(G). We give here very elementary and short proofs of main results of Rai.
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References
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Singh, S., Gumber, D. A note on commuting automorphisms of some finite p-groups. Math Notes 100, 755–757 (2016). https://doi.org/10.1134/S0001434616110146
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DOI: https://doi.org/10.1134/S0001434616110146