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Mathematical logic, algebra and number theory

On the commutation graph of cyclic TI-subgroup in an ortogonal group $G$

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 ortogonal group, 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 January 13, 2013, 01.03.2013