Geodesic
On the commutation graph of cyclic $TI$-subgroups in linear groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 114-120

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We study the commutation graph $\Gamma (A)$ of a 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 linear group, then the graph $\Gamma (A)$ is either a coclique or an edge-regular but not coedge-regular graph.
Keywords: finite group, cyclic $TI$-subgroup, commutation graph. 
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     title = {On the commutation graph of cyclic $TI$-subgroups in linear groups},
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N. D. Zyulyarkina. On the commutation graph of cyclic $TI$-subgroups in linear groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 114-120. http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a11/