An overview of graphs associated with character degrees and conjugacy class sizes in finite groups.

DOI10.1216/RMJ-2008-38-1-175zbMath1166.20006MaRDI QIDQ1010990

Mark L. Lewis

Publication date: 7 April 2009

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

finite groupssurvey articleconjugacy class sizescharacter degree graphs

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Ordinary representations and characters (20C15) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

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I ⋮ Finite groups whose prime graphs are regular. ⋮ Unnamed Item ⋮ Non-solvable groups whose character degree graph has a cut-vertex. II ⋮ The Taketa problem and character degree graphs with diameter three. ⋮ Character theory and categorification. Abstracts from the workshop held August 28 -- September 3, 2022 ⋮ Characters of prime power degree in principal blocks ⋮ Character graphs with diameter three ⋮ Conjugacy class sizes in arithmetic progression ⋮ Coloring of character graphs ⋮ An overview on the bipartite divisor graph for the set of irreducible character degrees ⋮ Prime graphs of finite groups with a small number of triangles. ⋮ CHARACTER GRAPHS WITH NONBIPARTITE HAMILTONIAN COMPLEMENT ⋮ Nonsolvable groups with no prime dividing three character degrees. ⋮ Recognition of the simple group \(\mathrm{PSL}(2,p^2)\) by character degree graph and order. ⋮ On cut vertices and eigenvalues of character graphs of solvable groups ⋮ Groups whose character degree graph has diameter three ⋮ Disconnected character graphs and odd dominating sets ⋮ Planar character-graphs ⋮ Fundamental groups of simplicial complexes ⋮ Bounding Fitting Heights of Two Classes of Character Degree Graphs ⋮ BIPARTITE DIVISOR GRAPH FOR THE PRODUCT OF SUBSETS OF INTEGERS ⋮ Finite nonsolvable groups whose character graphs have no triangles. ⋮ Hamiltonian character graphs ⋮ Five-vertex common divisor character degree graphs of non-solvable groups ⋮ Finite groups with three composite character degrees ⋮ Conjugacy classes contained in normal subgroups: an overview ⋮ Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements ⋮ Bipartite divisor graph for the set of irreducible character degrees ⋮ Classifying families of character degree graphs of solvable groups ⋮ On nonsolvable groups whose prime degree graphs have four vertices and one triangle ⋮ Recognition of the simple groups $PSL_2(q)$ by character degree graph and order ⋮ On bipartite divisor graph for character degrees ⋮ Finite Groups Whose Character Graphs Associated with Codegrees Have No Triangles ⋮ Degree graphs of simple groups. ⋮ The character degree simplicial complex of a finite group. ⋮ Character degrees, conjugacy class sizes, and element orders: three primes ⋮ On Huppert's rho-sigma conjecture ⋮ Character degree graphs of automorphism groups of characteristically simple groups ⋮ Solvable groups whose character degree graphs generalize squares ⋮ K₄-free character graphs with seven vertices ⋮ Groups whose bipartite divisor graph for character degrees has four or fewer vertices ⋮ On bipartite divisor graphs for group conjugacy class sizes. ⋮ Mathieu groups and its degree prime-power graphs ⋮ Finite Groups Whose Common-Divisor Graph is Regular ⋮ Groups whose vanishing class sizes are prime powers ⋮ Classifying character degree graphs with six vertices ⋮ Bounding the number of vertices in the degree graph of a finite group ⋮ 1-Connected character-graphs of finite groups with non-bipartite complement ⋮ Almost simple groups with no product of two primes dividing three character degrees ⋮ Co-degree graphs and order elements ⋮ Solvable groups whose prime divisor character degree graphs are 1-connected ⋮ Divisibility Graph for Symmetric and Alternating Groups ⋮ THE CHARACTER GRAPH OF A FINITE GROUP IS PERFECT ⋮ Character degree graphs that are complete graphs ⋮ On the character degree graph of finite groups ⋮ Regular character-graphs whose eigenvalues are greater than or equal to \(-2\) ⋮ Unnamed Item ⋮ On prime character degree graphs occurring within a family of graphs ⋮ Finite Groups Whose Character Degree Graphs Are Empty Graphs ⋮ On the character degree graph of solvable groups ⋮ 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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