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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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.
Action of a Frobenius-like group with kernel having central derived subgroup Ercan, Gülin (2016-09-01) 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 [F, h] = F for all nonidentity elements h is an element of H. Suppose that a finite group G admits a Frobenius-like group of auto-morphisms FH of coprime order with [F', H] = 1. In case where C-G( F) = 1 we prove that the groups G and C-G( H) have the same nilpotent length under certain additional assumptions.
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.