Geodesic
On the commutation graph of cyclic TI-subgroup in an ortogonal group~$G$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 180-199.

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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. 
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N. D. Zyulyarkina. On the commutation graph of cyclic TI-subgroup in an ortogonal group~$G$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 180-199. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a6/

[1] E. Artin, Geometricheskaya algebra, Nauka, M., 1969 | MR | Zbl

[2] N. D. Zyulyarkina, “Tsiklicheskie $TI$-podgruppy poryadka 4 v klassicheskikh gruppakh Shevalle nechetnoi kharakteristiki”, Voprosy algebry i logiki, Trudy IM SO RAN, 1996, 89–110 | Zbl

[3] N. D. Zyulyarkina, A. A. Makhnev, “Tsiklicheskie $TI$-podgruppy poryadka 4 v isklyuchitelnykh gruppakh Shevalle”, Trudy IMM UrO RAN, 3 (1994), 41–49 | MR

[4] A. A. Makhnev, “$TI$-podgruppy v gruppakh tipa kharakteristiki 2”, Mat. sbornik, 127 (1985), 239–244 | MR | Zbl

[5] M. E. Harris, “Finite groups containing an intrinsic $2$-component of Chevalley type over field of odd order”, Transactions of the American Math. Soc., 272:1 (1982), 1–65 | MR | Zbl