turkmath.org

A subgroup $H$ of a finite group $G$ is called a TNI-subgroup if $N_G(H)\cap H^g = 1$ for any $g \in G-N_G(H)$. I will present a recent result obtained in a joint research with Dr. Ercan concerning the structure of a finite group $G$ which has a subgroup $A$ of automorphisms of $G$ acting on $G$ in such a way that the centralizer of $A$ in $G$ is a TNI-subgroup of $G$. This generalizes some of the research about the groups admitting a fixed-point-free group of automorphisms.