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Minimal permutation representations of finite simple exceptional groups of types \(G_ 2\) and \(F_ 4\). (English. Russian original) Zbl 0880.20006
Algebra Logika 35, No. 6, 663-684 (1996); translation in Algebra Logic 35, No. 6, 371-383 (1996).
The present article continues works by V. D. Mazurov [Algebra Logika 32, No. 3, 267-287 (1993; Zbl 0854.20017)] and A. V. Vasil’ev and V. D. Mazurov [Algebra Logika 33, No. 6, 603-627 (1994; Zbl 0842.20015)] on minimal permutation representations of finite simple classical groups and sporadic groups. In the article under review minimal permutation representations of exceptional Chevalley groups of normal type \(G_2(q)\) and \(F_4(q)\) are studied. Degrees, stabilizers of points, ranks, subdegrees and double stabilizers are found.

20C33 Representations of finite groups of Lie type
20C34 Representations of sporadic groups
20E28 Maximal subgroups
20D06 Simple groups: alternating groups and groups of Lie type
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