Geodesic
Finite almost simple groups with prime graphs all of whose connected components are cliques
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 132-141 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We find finite almost simple groups with prime graphs all of whose connected components are cliques, i.e., complete graphs. The proof is based on the following fact, which was obtained by the authors and is of independent interest: the prime graph of a finite simple nonabelian group contains two nonadjacent odd vertices that do not divide the order of the outer automorphism group of this group.
Keywords: finite group, almost simple group, prime graph. 
@article{TIMM_2015_21_3_a14,
     author = {M. R. Zinov'eva and A. S. Kondrat'ev},
     title = {Finite almost simple groups with prime graphs all of whose connected components are cliques},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {132--141},
     year = {2015},
     volume = {21},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a14/}
}
TY  - JOUR
AU  - M. R. Zinov'eva
AU  - A. S. Kondrat'ev
TI  - Finite almost simple groups with prime graphs all of whose connected components are cliques
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2015
SP  - 132
EP  - 141
VL  - 21
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a14/
LA  - ru
ID  - TIMM_2015_21_3_a14
ER  - 
%0 Journal Article
%A M. R. Zinov'eva
%A A. S. Kondrat'ev
%T Finite almost simple groups with prime graphs all of whose connected components are cliques
%J Trudy Instituta matematiki i mehaniki
%D 2015
%P 132-141
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a14/
%G ru
%F TIMM_2015_21_3_a14
M. R. Zinov'eva; A. S. Kondrat'ev. Finite almost simple groups with prime graphs all of whose connected components are cliques. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 132-141. http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a14/

[1] Vasilev A.V., Vdovin E.P., “Kriterii smezhnosti v grafe prostykh chisel”, Algebra i logika, 44:6 (2005), 682–725 | MR | Zbl

[2] Vasilev A.V., Vdovin E.P., “Kokliki maksimalnogo razmera v grafe prostykh chisel konechnoi prostoi gruppy”, Algebra i logika, 50:4 (2011), 425–470 | MR | Zbl

[3] Zinoveva M.R., Mazurov V.D., “O konechnykh gruppakh s nesvyaznym grafom”, Trudy In-ta matematiki i mekhaniki UrO RAN, 18:3 (2012), 99–105

[4] Kondratev A.S., “O komponentakh grafa prostykh chisel konechnykh prostykh grupp”, Mat. sb., 180:6 (1989), 787–797 | MR | Zbl

[5] Kondratev A.S., Mazurov V.D., “Raspoznavanie znakoperemennykh grupp prostoi stepeni po poryadkam ikh elementov.”, Sib. mat. zhurn., 41:2 (2000), 359–369 | MR | Zbl

[6] Aschbacher M., Finite group theory, Cambridge Univ. Press, Cambridge, 1986, 274 pp. | MR | Zbl

[7] J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, Atlas of finite groups, Clarendon Press, Oxford, 1985, 252 pp. | MR | Zbl

[8] Gerono G.C., “Note sur la r$\acute{e}$solution en nombres entiers et positifs de l'$\acute{e}$quation $x^m=y^n+1$”, Nouv. Ann. Math. (2), 9 (1870), 469–471

[9] Gorenstein D., Lyons R., Solomon R., The classification of the finite simple groups, Number 3, Math. Surv. Monogr., 40, no. 3, Amer. Math. Soc., 1998, 420 pp. | MR

[10] Lucido M.S., “Prime graph components of finite almost simple groups”, Rend. Sem. Mat. Univ. Padova, 102 (1999), 1–22 ; addendum 107 (2002), 189–190 | MR | Zbl | MR | Zbl

[11] Lucido M.S., Moghaddamfar A.R., “Groups with complete prime graph connected components”, J. Group Theory, 7:3 (2004), 373–384 | DOI | MR | Zbl

[12] Williams J.S., “Prime graph components of finite groups”, J. Algebra, 69:2 (1981), 487–513 | DOI | MR | Zbl

[13] Zsigmondy K., “Zur Theorie der Potenzreste”, Monatsh. Math. Phys., 3 (1892), 265–284 | DOI | MR | Zbl