Regular orbits of linear groups with an application to the \(k(GV)\)-problem. I

DOI10.1006/jabr.1998.8078zbMath0970.20005OpenAlexW2916786178MaRDI QIDQ1569804

Dominic P. M. Goodwin

Publication date: 4 July 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.8078

zbMATH Keywords

defect groupsirreducible characters\(p\)-solvable groupsblocksregular orbitsquasi-simple groups\(k(GV)\)-problemfaithful modulesirreducible group actions

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Representations of finite groups of Lie type (20C33)

Related Items (19)

The solution of the \(k(GV)\)-problem. ⋮ Regular orbits of symmetric and alternating groups ⋮ Bases of twisted wreath products ⋮ On vanishing class sizes in finite groups ⋮ On the automorphism group of rational group algebras of finite groups ⋮ Generation of finite almost simple groups by conjugates. ⋮ Regular orbits of sporadic simple groups ⋮ Bases for quasisimple linear groups ⋮ The extraspecial case of the 𝑘(𝐺𝑉) problem ⋮ Arithmetic results on orbits of linear groups ⋮ Every coprime linear group admits a base of size two ⋮ The minimal base size for a 𝑝-solvable linear group ⋮ Orbit sizes and odd order composition factors of finite linear groups ⋮ Regular orbits of quasisimple linear groups. II ⋮ Regular orbits of quasisimple linear groups. I ⋮ On the codegrees of finite groups ⋮ Regular orbits of linear groups with an application to the \(k(GV)\)-problem. I ⋮ Regular orbits of linear groups with an application to the \(k(GV)\)-problem. II ⋮ The quasisimple case of the \(k(GV)\)-conjecture

Cites Work

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• The covering numbers of the sporadic simple groups
• A remark on Brauer's k(B)-conjecture
• On the minimal degrees of characters of \(S_n\)
• Hall-Higman type theorems. V
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• Generation of finite almost simple groups by conjugates.
• Regular orbits of linear groups with an application to the \(k(GV)\)-problem. I
• On the minimal degrees of projective representations of the finite Chevalley groups. II
• Regular orbits of linear groups
• On Brauer's \(k(B)\)-problem
• The quasisimple case of the \(k(GV)\)-conjecture
• Probabilistic generation of finite simple groups
• Products of conjugacy classes in groups
• The extraspecial case of the 𝑘(𝐺𝑉) problem
• ON THE NUMBER OF IRREDUCIBLE CHARACTERS OF FINITE GROUPS IN A GIVEN BLOCK
• On The Characters of p-Solvable Groups
• The Spin Representation of the Symmetric Group
• The local structure of finite groups of characteristic 2 type
• Fixed point free action with regular orbits.
• Generators for Finite Simple Groups, with Applications to Linear Groups
• On the Number of Characters in a Block and the k (GV ) PROBLEM FOR SELF-DUAL V

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