Good action of a nilpotent group with regular orbits

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2022-04-01

Author

Ercan, Gülin
GÜLOĞLU, İSMAİL ŞUAYİP

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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.

Subject Keywords

Fitting height, good action, nilpotent group, regular orbit

URI

https://hdl.handle.net/11511/97300

Journal

COMMUNICATIONS IN ALGEBRA

DOI

https://doi.org/10.1080/00927872.2022.2058008

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Department of Mathematics, Article

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A GENERALIZED FIXED-POINT-FREE ACTION Güloğlu, İsmail Şuayip; Ercan, Gülin (2013-05-01) 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.
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.
RELATIVE GROUP COHOMOLOGY AND THE ORBIT CATEGORY Pamuk, Semra (2014-07-03) Let G be a finite group and F be a family of subgroups of G closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative F-projective resolution for Z when F is the family of all subgroups HG with rkHrkG-1. We answer this question negatively by calculating the relative group cohomology FH*(G, ?(2)) where G = Z/2xZ/2 and F is the family of cyclic subgroups of G. To do this calculation we first observe that the relative group cohomology FH*(G, M) can be calc...
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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.

Citation Formats

G. Ercan and İ. Ş. GÜLOĞLU, “Good action of a nilpotent group with regular orbits,” COMMUNICATIONS IN ALGEBRA, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/97300.