Department of Mathematics
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Noncoprime action of a cyclic group
Ercan, Gülin; Güloğlu, İsmail Ş. (2024-04-01)
Let A be a finite nilpotent group acting fixed point freely on the finite (solvable) group G by automorphisms. It is conjectured that the nilpotent length of G is bounded above by ℓ(A), the number of primes dividing the or...
Nilpotent residual of a finite group
Rodrigues, Eliana; de Melo, Emerson; Ercan, Gülin (2024-03-01)
Let F be a nilpotent group acted on by a group H via automorphisms and let the group G admit the semidirect product FH as a group of automorphisms so that CG(F)=1. We prove that the order of γ∞(G), the rank of γ∞(G) are bo...
Commuting graph of a group action with few edges
Güloğlu, İsmail; Ercan, Gülin (2023-1-01)
Let A be a group acting by automorphisms on the group G. The commuting graph (Formula presented.) of A-orbits of this action is the simple graph with vertex set (Formula presented.), the set of all A-orbits on (Formula pre...
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 th...
Commuting graph of A-orbits
Gilloglu, Ismail S.; Ercan, Gülin (2021-05-01)
Let A be a finite group acting by automorphisms on the finite group G. We introduce the commuting graph Gamma(G, A) of this action and study some questions related to the structure of G under certain graph theoretical cond...
A Brief Note on the Noncoprime Regular Module Problem
Güloğlu, Ş.; Ercan, Gülin (2021-01-01)
We consider a special configuration in which a finite group A acts by automorphisms on a finite group G and the semidirect product GA acts on the vector space V by linear transformations and discuss the existence of a regu...
Good action on a finite group
Ercan, Gülin; Jabara, Enrico (Elsevier BV, 2020-10-01)
Let G and A be finite groups with A acting on G by automorphisms. In this paper we introduce the concept of "good action"; namely we say the action of A on G is good, if H = [H, B]C-H (B) for every subgroup B of A and ever...
Frobenius action on Carter subgroups
Ercan, Gülin (World Scientific Pub Co Pte Lt, 2020-08-01)
Let G he a finite solvable group and H be a subgroup of Aut(G). Suppose that there exists an H-invariant Carter subgroup F of G such that the semidirect product FH is a Frobenius group with kernel F and complement H. We pr...
On abelian group actions with TNI-centralizers
Ercan, Gülin (2019-07-03)
A subgroup H of a group G is said to be a TNI-subgroup if for any Let A be an abelian group acting coprimely on the finite group G by automorphisms in such a way that for all is a solvable TNI-subgroup of G. We prove that ...
Frobenius groups of automorphisms with almost fixed point free kernel
Ercan, Gülin (2019-03-01)
Let FH be a Frobenius group with kernel F and complement H, acting coprimely on the finite solvable group G by automorphisms. We prove that if C-G(H) is of Fitting length n then the index of the n-th Fitting subgroup F-n(G...
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