The semisimple conjugacy classes of finite groups of lie type E6and E7

DOI10.1080/00927879208824553zbMath0813.20015OpenAlexW2150164926MaRDI QIDQ4029180

Ingo Janiszczak, Peter Fleischmann

Publication date: 15 March 1993

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879208824553

zbMATH Keywords

Weyl groupfinite groups of Lie typesimple rootssemisimple conjugacy classes

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Simple groups: alternating groups and groups of Lie type (20D06) Representations of finite groups of Lie type (20C33)

Related Items (28)

The divisibility graph of finite groups of Lie type ⋮ Coxeter orbits and Brauer trees III ⋮ The semisimple conjugacy classes and the generic class number of the finite simple groups of lie type E₈ ⋮ On the computation of conjugacy classes of Chevalley groups ⋮ On the generating graph of direct powers of a simple group. ⋮ Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type. V: Mixed classes in Chevalley and Steinberg groups ⋮ On semi-rational finite simple groups ⋮ Maximal 2-local subgroups of \(F_4(q)\) and \(E_6^\eta(q)\). ⋮ Maximal 2-local subgroups of \(E_7(q)\). ⋮ Radical subgroups of the finite exceptional groups of Lie type \(E_6\). ⋮ On soluble subgroups of sporadic groups ⋮ Characteristic covering numbers of finite simple groups ⋮ Finite groups, 2-generation and the uniform domination number ⋮ Irreducible representations of odd degree ⋮ Thompson's conjecture for Lie type groups \(E_7(q)\). ⋮ Rouquier blocks in Chevalley groups of type \(E\). ⋮ Blocks with extraspecial defect groups of finite quasisimple groups. ⋮ On base sizes for algebraic groups ⋮ The Ore conjecture. ⋮ On base sizes for almost simple primitive groups ⋮ Combinatorics and Poincaré polynomials of hyperplane complements for exceptional Weyl groups ⋮ A computational approach to the Frobenius–Schur indicators of finite exceptional groups ⋮ Odd-Degree Characters and Self-Normalizing Sylow 2-Subgroups: A Reduction to Simple Groups ⋮ Finite fields, root systems, and orbit numbers of Chevalley groups ⋮ Imprimitive irreducible modules for finite quasisimple groups ⋮ The maximal subgroups of ⋮ Counting semisimple orbits of finite Lie algebras by genus ⋮ Finite groups have local non-Schur centralizers

Uses Software

• Maple

Cites Work

• Unnamed Item
• The centralizers of semisimple elements of the Chevalley groups \(E_ 7\) and \(E_ 8\)
• On the number of conjugacy classes in finite groups of lie type
• The möbius function of the lattice of closed subsystems of a root system

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