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

Journal

JOURNAL OF ALGEBRA AND ITS APPLICATIONS

DOI

https://doi.org/10.1142/s0219498812501721

Collections

Department of Mathematics, Article

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A generalized fixed point free automorphism of prime power order Ercan, Gülin (2012-06-01) Let G be a finite group and alpha be an automorphism of G of order p(n) for an odd prime p. Suppose that alpha acts fixed point freely on every alpha-invariant p'-section of G, and acts trivially or exceptionally on every elementary abelian alpha-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.
Action of a Frobenius-like group Güloǧlu, Ismail Ş.; Ercan, Gülin (2014-03-15) We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F, h] = F for all nonidentity elements h is an element of H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically closed field has an H-regular direct summand if either F is fixed point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of t...
Good action of a nilpotent group with regular orbits Ercan, Gülin; GÜLOĞLU, İSMAİL ŞUAYİP (2022-04-01) Suppose that A is a finite nilpotent group of odd order having a good action, in the sense of [1], on the group G of odd order. Under some additional assumptions we prove that the Fitting height of G is bounded above by the sum of the numbers of primes dividing vertical bar A vertical bar and vertical bar C-G(A)vertical bar counted with multiplicities.
NILPOTENT LENGTH OF A FINITE SOLVABLE GROUP WITH A FROBENIUS GROUP OF AUTOMORPHISMS Ercan, Gülin; Ogut, Elif (2014-01-01) We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C-CG(F) (h) = 1 for all nonidentity elements h is an element of H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.

Citation Formats

İ. Ş. Güloğlu and G. Ercan, “A GENERALIZED FIXED-POINT-FREE ACTION,” JOURNAL OF ALGEBRA AND ITS APPLICATIONS, pp. 0–0, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42052.