THE INFLUENCE OF CONJUGACY CLASS SIZES ON THE STRUCTURE OF FINITE GROUPS: A SURVEY

DOI10.1142/S1793557111000459zbMath1257.20030MaRDI QIDQ2892236

Alan R. Camina, Rachel D. Camina

Publication date: 18 June 2012

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

finite solvable groupsnumbers of conjugacy classesfinite groupsfinite \(p\)-groupscommon divisor graphs

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Finite nilpotent groups, (p)-groups (20D15) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items (41)

Graphs attached to simple Frobenius-Perron dimensions of an integral fusion category ⋮ Notes on conjugacy classes of finite groups ⋮ The divisibility graph of finite groups of Lie type ⋮ Coprime action and arithmetical conditions on invariant conjugacy classes. ⋮ PGL2(q) cannot be determined by its cs ⋮ On the class of KN-complete groups ⋮ Implications of the index of a fixed point subgroup ⋮ Lengths of conjugacy classes of π-elements and primary elements in finite groups ⋮ Groups whose vanishing class sizes are p-powers ⋮ Unnamed Item ⋮ The set of conjugacy class sizes of a finite group does not determine its solvability. ⋮ ON SUB-CLASS SIZES OF FINITE GROUPS ⋮ Unnamed Item ⋮ Nilpotent Lie algebras of breadth type (0, 3) ⋮ On products of groups and indices not divisible by a given prime ⋮ Conjugacy class sizes in arithmetic progression ⋮ On the regularity of a graph related to conjugacy classes of groups. ⋮ Groups with some arithmetic conditions on real class sizes. ⋮ A note on conjugacy classes of finite groups. ⋮ ON CONJUGACY CLASS SIZES AND CHARACTER DEGREES OF FINITE GROUPS ⋮ On solvable groups with one vanishing class size ⋮ On the structure of a mutually permutable product of finite groups ⋮ BIPARTITE DIVISOR GRAPH FOR THE PRODUCT OF SUBSETS OF INTEGERS ⋮ On groups where the twisted conjugacy class of the unit element is a subgroup ⋮ Conjugacy classes contained in normal subgroups: an overview ⋮ Unnamed Item ⋮ Finite groups with the same conjugacy class sizes as a finite simple group ⋮ One-prime power hypothesis for conjugacy class sizes ⋮ On finite groups with square-free conjugacy class sizes ⋮ Groups with vanishing class size \(p\) ⋮ Some results on relative commutativity degree. ⋮ On sub-class sizes of mutually permutable products ⋮ Non-solvable groups and the two-prime hypothesis on conjugacy class sizes ⋮ Groups whose vanishing class sizes are prime powers ⋮ Unnamed Item ⋮ Divisibility Graph for Symmetric and Alternating Groups ⋮ The prime graph on class sizes of a finite group has a bipartite complement ⋮ ON THE REGULAR GRAPH RELATED TO THE G-CONJUGACY CLASSES ⋮ The divisibility graph for F-groups ⋮ Transposable character tables and group duality ⋮ Groups having complete bipartite divisor graphs for their conjugacy class sizes.

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