Mathematical logic, algebra and number theory

On the commutation graph of cyclic $TI$-subgroup in a symmetric group

N. D. Zyulyarkina

South Ural State University, Chelyabinsk

Abstract: We study the commutation graph $\Gamma _G(A)$ of cyclic $TI$-subgroup A of order 4 in a finite group $G$ with quasisimple generalized Fitting subgroup $F^*(G)$. It is proved that, if $F^*(G)$ is a covering group for $A_n$, then the graph $\Gamma _G(A)$ is edge-regular but not coedge-regular graph.

Keywords: finite group, cyclic $TI$-subgroup, commutation graph.

UDC: 519.17+512.54

MSC: 05C25

Received May 1, 2013, published May 22, 2013