Huppert's conjecture for alternating groups

DOI10.1016/j.jalgebra.2016.09.012zbMath1361.20013arXiv1502.03425OpenAlexW2963676563WikidataQ123364641 ScholiaQ123364641MaRDI QIDQ335613

Christine Bessenrodt, Hung P. Tong-Viet, Ji Ping Zhang

Publication date: 2 November 2016

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.03425

zbMATH Keywords

alternating groupscharacter degreesHuppert's conjectures

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Representations of finite symmetric groups (20C30) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (12)

Groups with sharp non-linear irreducible characters ⋮ A new characterization of the automorphism groups of Mathieu groups ⋮ A characterization of the simple Ree groups \(^2 F_4( q^2)\) by their character codegrees ⋮ 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 ⋮ Huppert's conjecture and almost simple groups ⋮ Some nonsolvable character degree sets ⋮ Degrees of irreducible representations of direct products of nonabelian simple groups ⋮ Extending Huppert's conjecture to almost simple groups of Lie type ⋮ Mathieu groups and its degree prime-power graphs ⋮ Some character degree sets implying nonsolvability ⋮ Recognition of \(\mathrm{PSL}(2, p^2)\) by order and some properties on character degrees

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Alternating and sporadic simple groups are determined by their character degrees.
• Symmetric groups are determined by their character degrees.
• Dimensions of the irreducible representations of the symmetric and alternating group
• Recovering information about a group from its complex group algebra
• The minimal degree of a non-linear irreducible character of a solvable group
• On the minimal degrees of characters of \(S_n\)
• Some simple groups which are determined by the set of their character degrees. I
• Complex group algebras of the double covers of the symmetric and alternating groups.
• An answer to a question of Isaacs on character degree graphs.
• A reduction theorem for the McKay conjecture.
• The non-coprime \(k(GV)\) problem.
• Nonsolvable groups with few character degrees.
• Nilpotent and perfect groups with the same set of character degrees
• PRIME POWER DEGREE REPRESENTATIONS OF THE SYMMETRIC AND ALTERNATING GROUPS
• Prime Power Degree Representations of the Double Covers of the Symmetric and Alternating Groups
• On Huppert's Conjecture for Alternating Groups of Low Degrees
• The set of character degrees of a finite group does not determine its solvability

This page was built for publication: Huppert's conjecture for alternating groups