# ON AUTOMORPHISMS OF FINITE GROUPS

@inproceedings{Horoevski1974ONAO, title={ON AUTOMORPHISMS OF FINITE GROUPS}, author={M V Horo{\vs}evskiĭ}, year={1974} }

- Published 1974
DOI:10.1070/SM1974v022n04ABEH001707

We consider orbits of elements of a finite group G with respect to the action on G of a cyclic automorphism group generated by . We obtain sufficient conditions for the existence of an orbit whose length is equal to the order of the automorphism . Namely, such an orbit exists for any automorphism of a semisimple or nilpotent finite group G and for an automorphism of an arbitrary finite group G when the orders of and G are relatively prime. In the general case, the question of the existence of… CONTINUE READING

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## On finite groups where the order of every automorphism is a cycle length

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