On finite \(p\)-groups which have only two conjugacy lengths

DOI10.1007/BF02773158zbMath1003.20022MaRDI QIDQ1601469

Kenta Ishikawa

Publication date: 28 October 2002

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

conjugacy classesfinite \(p\)-groups

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Finite nilpotent groups, (p)-groups (20D15)

Related Items (29)

Groups with few class sizes and the centraliser equality subgroup. ⋮ THE INFLUENCE OF CONJUGACY CLASS SIZES ON THE STRUCTURE OF FINITE GROUPS: A SURVEY ⋮ Characterizations of some groups in terms of centralizers ⋮ Counting centralizers and z-classes of some F-groups ⋮ CONJUGACY CLASS SIZES IN FINITE GROUPS ⋮ Finite \(p\)-groups of nilpotency class 3 with two conjugacy class sizes ⋮ Conjugacy classes of small size in solvable groups ⋮ Finite groups whose noncentral class sizes have the same \(p\)-part for some prime \(p\). ⋮ Finite \(p\)-groups of conjugate type \(\{1,p^{3}\}\) ⋮ Subgroups generated by small classes in finite groups ⋮ On \(p\)-index extremal groups ⋮ Unnamed Item ⋮ Nilpotent Lie algebras of breadth type (0, 3) ⋮ Influence of conjugacy class sizes of some elements on the structure of a finite group ⋮ Spreads and nilpotence class in nilpotent groups and Lie algebras. ⋮ CONJUGACY CLASS SIZES OF CERTAIN DIRECT PRODUCTS ⋮ On solvable groups with one vanishing class size ⋮ On the normal subgroup with minimal \(G\)-conjugacy class sizes ⋮ On the probability distribution associated to commutator word map in finite groups ⋮ FINITE GROUPS WHOSE NONCENTRAL COMMUTING ELEMENTS HAVE CENTRALIZERS OF EQUAL SIZE ⋮ Non-commuting graph of a group. ⋮ Groups with vanishing class size \(p\) ⋮ Some results on relative commutativity degree. ⋮ The structure of finite groups with three class sizes ⋮ Elements of minimal breadth in finite p-groups and lie algebras ⋮ On Subgroups Generated by Small Classes in Finite Groups ⋮ Derived length and conjugacy class sizes. ⋮ Lie algebras with few centralizer dimensions. ⋮ Powers of irreducible characters and conjugacy classes in finite groups

Cites Work

• Unnamed Item
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• Character theory of finite groups
• Finite \(p\)-groups up to isoclinism, which have only two conjugacy lengths
• A characterization of groups in terms of the degrees of their characters. II
• Groups with many equal classes
• On Finite Groups with Given Conjugate Types I

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