On the average character degree of finite groups

DOI10.1112/blms/bdt107zbMath1335.20007arXiv1309.0173OpenAlexW1982897585MaRDI QIDQ5419231

Hung Ngoc Nguyen, Alexander Moretó

Publication date: 6 June 2014

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

Full work available at URL: https://arxiv.org/abs/1309.0173

zbMATH Keywords

finite groupssolvabilityirreducible complex charactersaverage character degree

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Probabilistic methods in group theory (20P05)

Related Items (20)

The character degree ratio and composition factors of a finite group. ⋮ The degrees of non-monomial characters and solvability of a finite group ⋮ On the average degree of some irreducible characters of a finite group ⋮ Unnamed Item ⋮ The average character degree of finite groups and Gluck's conjecture ⋮ Irreducible characters of even degree and normal Sylow 2-subgroups ⋮ On the average codegree of a finite group ⋮ Supersolvability and nilpotency in terms of the commuting probability and the average character degree ⋮ The average element order and the number of conjugacy classes of finite groups ⋮ On the average character degree and the average class size in finite groups. ⋮ Variations on average character degrees and \(p\)-nilpotence ⋮ Average number of zeros of characters of finite groups ⋮ On the sum of character degrees coprime to \(p\) and \(p\)-nilpotency of finite groups ⋮ Two results on the character degree sums ⋮ Finite groups with an irreducible character of large degree. ⋮ The average character degree and an improvement of the Itô-Michler theorem ⋮ Strong subgroup commutativity degree and some recent problems on the commuting probabilities of elements and subgroups ⋮ On the \({p}\)-closedness and \({p}\)-nilpotency of finite groups ⋮ Finite groups with few character zeros ⋮ On the existence of Johnson polynomials for nilpotent groups.

Cites Work

• Unnamed Item
• Unnamed Item
• The average degree of an irreducible character of a finite group.
• Real characters of \(p'\)-degree.
• Character degree sums of finite groups.
• A characterization of groups in terms of the degrees of their characters
• A characterization of groups in terms of the degrees of their characters. II
• Character degree sums in finite nonsolvable groups
• Character degree graphs that are complete graphs

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