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Minimal permutation representations of finite simple exceptional groups of types \(E_6\), \(E_7\), and \(E_8\). (English. Russian original) Zbl 0941.20006
Algebra Logika 36, No. 5, 518-530 (1997); translation in Algebra Logic 36, No. 5, 302-310 (1997).
Summary: The article continues the author’s paper [Algebra Logika 35, No. 6, 663-684 (1996; Zbl 0880.20006)]. A minimal permutation representation of a group is a faithful permutation representation of least degree. We find degrees and point stabilizers, as well as ranks, subdegrees, and two-point stabilizers, for groups of types \(E_6\), \(E_7\), and \(E_8\). This closes the study of minimal permutation representations of finite simple Chevalley groups.

MSC:
20C33 Representations of finite groups of Lie type
20G05 Representation theory for linear algebraic groups
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