Prime graph components of finite simple groups
Sbornik. Mathematics, Tome 67 (1990) no. 1, pp. 235-247 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G$ be a finite group and $\pi(G)$ the set of prime factors of its order. The prime graph of $G$ is the graph with vertex-set $\pi(G)$, two vertices $p$ and $q$ being joined by an edge whenever $G$ contains an element of order $pq$. This article contains an explicit description of the primes in each of the connected components of the prime graphs of the finite simple groups of Lie type of even characteristic. This solves question 9.16 of the “Kourovka Notebook”. Bibliography: 15 titles.
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A. S. Kondrat'ev. Prime graph components of finite simple groups. Sbornik. Mathematics, Tome 67 (1990) no. 1, pp. 235-247. http://geodesic.mathdoc.fr/item/SM_1990_67_1_a13/

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

[2] Gruenberg K. W., Roggenkamp K. W., “Decomposition of the augmentation ideal and of the relation modules of a finite group”, Proc. London Math. Soc., 31:2 (1975), 149–166 | DOI | MR | Zbl

[3] Kourovskaya tetrad, In-t matematiki SO AN SSSR, Novosibirsk, 1984

[4] Kondratev A. S., “Podgruppy konechnykh grupp Shevalle”, UMN, 41:1 (1986), 57–96 | MR | Zbl

[5] Steinberg R., Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR | Zbl

[6] Seminar po algebraicheskim gruppam, Mir, M., 1975

[7] Gorenstein D., Finite groups, Harper and Row, New York, 1968 | MR | Zbl

[8] Hering Ch., “Transitive linear groups and linear groups which contain irreducible subgroups of prime order”, Geom. Dedic., 2:4 (1974), 425–460 | DOI | MR | Zbl

[9] Aschbacher M., Seitz G. M., “Involutions in Chevalley groups over fields of even order”, Nagoya Math. J., 63 (1976), 1–92 | MR

[10] Dye R. H., “On the involution classes of the linear groups $\operatorname{GL}_n(K)$, $\operatorname{SL}_n(K)$, $\operatorname{PGL}_n(K)$, $\operatorname{PSL}_n(K)$ over fields of characteristic two”, Proc. Cambridge Phil. Soc., 72:1 (1972), 1–6 | DOI | MR | Zbl

[11] Dye R. H., “On the conjugacy classes of involutions of the unitary groups $\operatorname{U}_m(K)$, $\operatorname{SU}_m(K)$, $\operatorname{PU}_m(K)$, $\operatorname{PSU}_m(K)$ over perfect fields of characteristic $2$”, J. Algebra., 24:3 (1973), 453–459 | DOI | MR | Zbl

[12] Carter R. W., “Conjugacy classes in the Weyl group”, Compositio Math., 25:1 (1972), 1–59 | MR | Zbl

[13] Seitz G. M., “On the subgroup structure of classical groups”, Commun. Algebra, 10:8 (1982), 875–885 | DOI | MR | Zbl

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

[15] Gorenstein D., Lyons R., The local structure of finite groups of characteristic $2$ type, Mem. Amer. Math. Soc., 276, 1983 | MR | Zbl