Geodesic
On the commutation graph of cyclic TI-subgroup in an ortogonal group $G$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 180-199 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SEMR_2013_10_a6,
     author = {N. D. Zyulyarkina},
     title = {On the commutation graph of cyclic {TI-subgroup} in an ortogonal group~$G$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {180--199},
     year = {2013},
     volume = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a6/}
}
TY  - JOUR
AU  - N. D. Zyulyarkina
TI  - On the commutation graph of cyclic TI-subgroup in an ortogonal group $G$
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2013
SP  - 180
EP  - 199
VL  - 10
UR  - http://geodesic.mathdoc.fr/item/SEMR_2013_10_a6/
LA  - ru
ID  - SEMR_2013_10_a6
ER  - 
%0 Journal Article
%A N. D. Zyulyarkina
%T On the commutation graph of cyclic TI-subgroup in an ortogonal group $G$
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2013
%P 180-199
%V 10
%U http://geodesic.mathdoc.fr/item/SEMR_2013_10_a6/
%G ru
%F SEMR_2013_10_a6
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