Signed permutation modules, Singer cycles and class numbers

DOI10.1515/JGT.2010.048zbMath1258.20001OpenAlexW2076670131MaRDI QIDQ3007957

Peter Schmid

Publication date: 17 June 2011

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jgt.2010.048

zbMATH Keywords

numbers of conjugacy classesSinger cyclesfinite group actions\(k(GV)\)-problemsolvable permutation groupscharacter congruences

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Ordinary representations and characters (20C15) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Modular representations and characters (20C20) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Related Items

Finite groups satisfying character degree congruences, On blocks with abelian defect groups of small rank, On the number of conjugacy classes of a permutation group.

Cites Work

• A remark on Brauer's k(B)-conjecture
• Linear groups containing a Singer cycle
• On the number of conjugacy classes of a finite group
• Upper bounds for the number of conjugacy classes of a finite group
• Real vectors for linear groups and the \(k(GV)\)-problem
• The \(k(GV)\) conjecture for modules in characteristic 31
• On Brauer's \(k(B)\)-problem for blocks of \(p\)-solvable groups with non-Abelian defect groups.
• On Brauer's \(k(B)\)-problem
• The solution of the \(k(GV)\)-problem.
• The non-coprime \(k(GV)\) problem.
• Bounding the number of conjugacy classes of a permutation group
• Minimal characters of the finite classical groups
• Some remarks on the k(GV ) theorem