Abstract
Let σ be an automorphism of a finite group G and suppose that σ fixes every element of G that has prime order or order 4. The main result of this paper shows that the structure of the subgroup H=[G, σ] is severely limited in terms of the order n of σ. In particular, H has exponent dividing n and it is nilpotent of class bounded in terms of n.
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References
H.-W. Henn and S. Priddy, p-nilpotence, classifying space indecomposability, and other properties of almost all finite groups. Comment. Math. Helv. 69, 335–350 (1994).
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Isaacs, I.M. Automorphisms fixing elements of prime order in finite groups. Arch. Math. 68, 359–366 (1997). https://doi.org/10.1007/s000130050068
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DOI: https://doi.org/10.1007/s000130050068