A GENERALIZED FIXED-POINT-FREE ACTION

Date

2013-05-01

Author

Güloğlu, İsmail Şuayip
Ercan, Gülin

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In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x epsilon C-G(A) of prime order or of order 4, every conjugate of x in G is also contained in C-G(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.

Subject Keywords

Solvable, Nilpotent height, Automorphism, Fixed point free action

URI

https://hdl.handle.net/11511/42052

Collections

Department of Mathematics, Article