On groups with conjugacy classes of distinct sizes.

DOI10.1016/J.JALGEBRA.2004.03.029zbMath1077.20022OpenAlexW2087800440MaRDI QIDQ1763901

Avital Oliver, Zvi Arad, Mikhail E. Muzychuk

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.03.029

zbMATH Keywords

rational groupsminimal counterexamplenon-Abelian composition factors\(S_3\)-conjectureanti-homogeneous groupsconjugacy classes of distinct sizesnon-Abelian socles

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Ordinary representations and characters (20C15) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Finite simple groups and their classification (20D05)

Cites Work

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• On finite rational groups and related topics
• Finite groups in which no two distinct conjugacy classes have the same order
• On a generalisation of F. M. Markel' theorem
• Groups whose characters are rational-valued
• Finite groups with many conjugate elements
• The \(S_ 3\)-conjecture for solvable groups
• Groups with many conjugate elements
• On finite groups with given conjugate types. II
• On finite groups with given conugate types. III
• \(k\)-homogeneous groups
• Finite Groups with a given Number of Conjugate Classes
• On Finite Groups with Given Conjugate Types I

Related Items (2)

THE INFLUENCE OF CONJUGACY CLASS SIZES ON THE STRUCTURE OF FINITE GROUPS: A SURVEY ⋮ Multiplicities of fields of values of irreducible characters of finite groups

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