On the influence of fixed point free nilpotent automorphism groups

Date

2017-12-01

Author

Ercan, Gülin
Güloğlu, İsmail Şuayip

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A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that for all nonidentity elements . Let FH be a Frobenius-like group with complement H of prime order such that is of prime order. Suppose that FH acts on a finite group G by automorphisms where in such a way that In the present paper we prove that the Fitting series of coincides with the intersections of with the Fitting series of G, and the nilpotent length of G exceeds the nilpotent length of by at most one. As a corollary, we also prove that for any set of primes , the upper -series of coincides with the intersections of with the upper -series of G, and the - length of G exceeds the -length of by at most one.

Subject Keywords

Frobenius-like group, Fixed points, Nilpotent length, Pi-length

URI

https://hdl.handle.net/11511/44093

Collections

Department of Mathematics, Article