Finite groups whose irreducible characters vanish only on \(p\)-elements.

DOI10.1016/j.jpaa.2008.07.001zbMath1162.20004OpenAlexW1965748276MaRDI QIDQ2378549

Silvio Dolfi, Pablo Spiga, Daniela Bubboloni

Publication date: 8 January 2009

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2008.07.001

zbMATH Keywords

finite groupsirreducible characters\(p\)-elementsvanishing elements

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20)

Related Items (15)

Primitive permutation groups and derangements of prime power order. ⋮ A generalization of strongly monomial groups ⋮ Groups whose vanishing elements are of odd order ⋮ Fixed-point-free elements in \(p\)-groups. ⋮ A new characterization of Suzuki’s simple groups ⋮ Finite groups with some restriction on the vanishing set ⋮ Class product and character product. ⋮ On the vanishing prime graph of solvable groups ⋮ On the orders of vanishing elements of finite groups ⋮ Recognition of some finite simple groups by the orders of vanishing elements ⋮ Groups with vanishing class size \(p\) ⋮ On the orders of zeros of irreducible characters. ⋮ Finite groups whose real-valued irreducible characters have prime power degrees ⋮ Real ordinary characters and real Brauer characters ⋮ A new characterization of some finite simple groups.

Cites Work

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• Transitive permutation groups in which all derangements are involutions.
• Character degrees, class sizes, and normal subgroups of a certain class of \(p\)-groups
• Groups with some combinatorial properties
• Finite groups admitting a fixed-point-free automorphism group
• Finite group elements where no irreducible character vanishes
• On vanishing sums of roots of unity.
• Normal \(p\)-complements and irreducible characters
• Irreducible restriction and zeros of characters
• Zeros of characters of finite groups

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