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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.

MSC:
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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