On the Number of Components of a Graph Related to Character Degrees

DOI10.2307/2047522zbMath0645.20005OpenAlexW4246572350MaRDI QIDQ3788181

Olaf Manz, Wolfgang Willems, Reiner Staszewski

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2047522

zbMATH Keywords

connected componentsfinite groupsirreducible complex characters

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Finite simple groups and their classification (20D05)

Related Items (58)

Graphs attached to simple Frobenius-Perron dimensions of an integral fusion category ⋮ Recognition of \(\mathrm{PSL}(2,2)^a)\) by the orders of vanishing elements ⋮ Bounding graph diameters of nonsolvable groups. ⋮ Groups which do not have four irreducible characters of degrees divisible by a prime \(p\) ⋮ Nonsolvable normal subgroups and irreducible character degrees. ⋮ Simple groups and strong covers. ⋮ Recognition of Janko groups and some simple $K_4$-groups by the order and one irreducible character degree or character degree graph ⋮ Nonsolvable groups satisfying the one-prime hypothesis. ⋮ Simple groups and the two-prime hypothesis ⋮ Unnamed Item ⋮ n-Exact character graphs ⋮ Finite solvable groups whose character graphs are trees. ⋮ A class of finite groups with complete character degree graphs. ⋮ A new characterization of the automorphism groups of Mathieu groups ⋮ Graphs of nonsolvable groups with four degree-vertices. ⋮ Non-solvable groups whose character degree graph has a cut-vertex. I ⋮ Regular character degree graphs. ⋮ 5-regular prime graphs of finite nonsolvable groups ⋮ Character theory and categorification. Abstracts from the workshop held August 28 -- September 3, 2022 ⋮ Connectedness of degree graphs of nonsolvable groups. ⋮ On groups with the same character degrees as almost simple groups with socle small Ree groups ⋮ Groups with the same character degrees as almost simple Suzuki groups ⋮ Prime divisors of character degrees ⋮ Character graphs with diameter three ⋮ Five-vertex degree graphs of nonsolvable groups ⋮ Alternating and sporadic simple groups are determined by their character degrees. ⋮ Finite groups whose irreducible Brauer characters have prime power degrees. ⋮ Primes dividing the degrees of the real characters. ⋮ Character degrees of simple groups ⋮ CHARACTER GRAPHS WITH NONBIPARTITE HAMILTONIAN COMPLEMENT ⋮ Nonsolvable groups with no prime dividing three character degrees. ⋮ The co-degrees of irreducible characters ⋮ Zeros of Brauer characters and the defect zero graph ⋮ Nonsolvable groups satisfying the prime-power hypothesis. ⋮ Recognition of the simple group \(\mathrm{PSL}(2,p^2)\) by character degree graph and order. ⋮ Disconnected character graphs and odd dominating sets ⋮ A characterization of linear groups \(L_3(q)\) by their character degree graphs and orders ⋮ Simple groups with few irreducible character degrees ⋮ Planar character-graphs ⋮ Degree graphs of simple orthogonal and symplectic groups. ⋮ Finite nonsolvable groups whose character graphs have no triangles. ⋮ Hamiltonian character graphs ⋮ Bounding graph diameters of solvable groups. ⋮ Five-vertex common divisor character degree graphs of non-solvable groups ⋮ Diameters of degree graphs of nonsolvable groups. ⋮ Recognition of the simple groups $PSL_2(q)$ by character degree graph and order ⋮ Degree graphs of simple groups. ⋮ An overview of graphs associated with character degrees and conjugacy class sizes in finite groups. ⋮ Solvable groups whose character degree graphs generalize squares ⋮ K₄-free character graphs with seven vertices ⋮ Applications of a graph related to conjugacy classes in finite groups ⋮ Mathieu groups and its degree prime-power graphs ⋮ Finite Groups Whose Common-Divisor Graph is Regular ⋮ 1-Connected character-graphs of finite groups with non-bipartite complement ⋮ Almost simple groups with no product of two primes dividing three character degrees ⋮ Solvable groups whose prime divisor character degree graphs are 1-connected ⋮ THE CHARACTER GRAPH OF A FINITE GROUP IS PERFECT ⋮ Regular character-graphs whose eigenvalues are greater than or equal to \(-2\)

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