Good action of a nilpotent group with regular orbits

Download
2022-04-01
Ercan, Gülin
GÜLOĞLU, İSMAİL ŞUAYİP
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.
COMMUNICATIONS IN ALGEBRA

Suggestions

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...
On local finiteness of periodic residually finite groups
Kuzucouoglu, M; Shumyatsky, P (2002-10-01)
Let G be a periodic residually finite group containing a nilpotent subgroup A such that C-G (A) is finite. We show that if [A, A(g)] is finite for any g is an element of G, then G is locally finite.
Prime graphs of solvable groups
Ulvi , Muhammed İkbal; Ercan, Gülin; Department of Electrical and Electronics Engineering (2020-8)
If $G$ is a finite group, its prime graph $Gamma_G$ is constructed as follows: the vertices are the primes dividing the order of $G$, two vertices $p$ and $q$ are joined by an edge if and only if $G$ contains an element of order $pq$. This thesis is mainly a survey that gives some important results on the prime graphs of solvable groups by presenting their proofs in full detail.
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.