A generalized fixed point free automorphism of prime power order
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CitationERCAN, G., GÜLOĞLU, İ.Ş. (2012). A generalized fixed point free automorphism of prime power order. International Journal of Algebra and Computation, 22 (4), pp. 1250029-1-1250029-5. https://dx.doi.org/10.1142/S0218196712500294
Let G be a finite group and α be an automorphism of G of order pn for an odd prime p. Suppose that α acts fixed point freely on every α-invariant p′-section of G, and acts trivially or exceptionally on every elementary abelian α-invariant p-section of G. It is proved that G is a solvable p-nilpotent group of nilpotent length at most n + 1, and this bound is best possible.