Elements of minimal breadth in finite p-groups and lie algebras

DOI10.1017/S1446788700015834zbMath1115.20017WikidataQ115335586 ScholiaQ115335586MaRDI QIDQ3412786

Avinoam Mann

Publication date: 2 January 2007

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

conjugacy classesfinite \(p\)-groupsnilpotent Lie algebrasminimal elementsbreadthsminimal classes

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Generators, relations, and presentations of groups (20F05) Finite nilpotent groups, (p)-groups (20D15) Solvable, nilpotent (super)algebras (17B30)

Related Items (16)

THE INFLUENCE OF CONJUGACY CLASS SIZES ON THE STRUCTURE OF FINITE GROUPS: A SURVEY ⋮ Subgroups generated by small classes in finite groups ⋮ Influence of conjugacy class sizes of some elements on the structure of a finite group ⋮ Group-theoretic generalisations of vertex and edge connectivities ⋮ Spreads and nilpotence class in nilpotent groups and Lie algebras. ⋮ CONJUGACY CLASS SIZES OF CERTAIN DIRECT PRODUCTS ⋮ On a conjecture of A. Mann ⋮ Universal commutator relations, Bogomolov multipliers, and commuting probability ⋮ FINITE GROUPS WHOSE NONCENTRAL COMMUTING ELEMENTS HAVE CENTRALIZERS OF EQUAL SIZE ⋮ The breadth-degree type of a finite \(p\)-group ⋮ On bipartite divisor graphs for group conjugacy class sizes. ⋮ Lie algebras with few centralizers ⋮ Groups where the centers of the irreducible characters form a chain. II ⋮ Some unsolvable conjectures in finite \(p\)-groups ⋮ On Subgroups Generated by Small Classes in Finite Groups ⋮ CORRECTION TO ‘CONJUGACY CLASS SIZES IN FINITE GROUPS’

Cites Work

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• On finite \(p\)-groups which have only two conjugacy lengths
• Finite \(p\)-groups up to isoclinism, which have only two conjugacy lengths
• Lie algebras with few centralizer dimensions.
• Groups with few class sizes and the centraliser equality subgroup.
• Sets of $p$-powers as conjugacy class sizes

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