On vanishing criteria that control finite group structure

DOI10.1016/j.jalgebra.2016.03.030zbMath1353.20014arXiv1509.06571OpenAlexW2903876254MaRDI QIDQ290427

Julian M. A. Brough

Publication date: 1 June 2016

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

Full work available at URL: https://arxiv.org/abs/1509.06571

zbMATH Keywords

conjugacy classesnilpotent groupssolvable groupssupersolvable groups\(p\)-groupscharacter valuescharacters of defect zeroFitting groupsformations of groups

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Ordinary representations and characters (20C15) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Special subgroups (Frattini, Fitting, etc.) (20D25) Modular representations and characters (20C20) Finite simple groups and their classification (20D05) Finite nilpotent groups, (p)-groups (20D15)

Related Items (15)

Vanishing elements and Sylow subgroups ⋮ Finite groups with at most six vanishing conjugacy classes ⋮ Groups whose vanishing elements are of odd order ⋮ On vanishing class sizes in finite groups ⋮ SOME PRODUCTS OF SUBGROUPS AND VANISHING CONJUGACY CLASS SIZES ⋮ Finite groups with some restriction on the vanishing set ⋮ Non-vanishing elements in finite groups. ⋮ Zeros of irreducible characters in factorised groups ⋮ On solvable groups with one vanishing class size ⋮ On the orders of vanishing elements of finite groups ⋮ ON VANISHING CRITERIA THAT CONTROL FINITE GROUP STRUCTURE II ⋮ On finite groups with square-free conjugacy class sizes ⋮ Groups whose vanishing class sizes are prime powers ⋮ Non-solvable groups each of whose vanishing class sizes has at most two prime divisors ⋮ A note on class sizes of vanishing elements in finite groups

Cites Work

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• Finite group elements where no irreducible character vanishes
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• Normalteiler und maximale Untergruppen endlicher Gruppen
• Character degree graphs that are complete graphs
• Remarks on the length of conjugacy classes of finite groups
• Defect zero blocks for finite simple groups
• Endliche Gruppen I
• Arithmetical Conditions on the Conjugacy Class Numbers of a Finite Group

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