Geodesic
Groups in which Raising to a Power is an Automorphism
Canadian mathematical bulletin, Tome 8 (1965) no. 6, pp. 825-827

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For any group G and integer n, let Pn:G→G be the function defined by Pn(g) = gn for all g ε G. If G is abelian then Pn is a homomorphism for all n. Conversely, it is well known (and easy to show) that if P2 or P-1 is a homomorphism then G is abelian. As the groups Gn described below show, for every n other than 2 and -1 there exist non-abelian groups for which Pn is a homomorphism. 
Trotter, H. F. Groups in which Raising to a Power is an Automorphism. Canadian mathematical bulletin, Tome 8 (1965) no. 6, pp. 825-827. doi: 10.4153/CMB-1965-063-4
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     author = {Trotter, H. F.},
     title = {Groups in which {Raising} to a {Power} is an {Automorphism}},
     journal = {Canadian mathematical bulletin},
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     year = {1965},
     volume = {8},
     number = {6},
     doi = {10.4153/CMB-1965-063-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-063-4/}
}
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