Symmetric groups are determined by their character degrees.

DOI10.1016/j.jalgebra.2010.11.018zbMath1246.20007arXiv1103.3939OpenAlexW2040868793MaRDI QIDQ653387

Hung P. Tong-Viet

Publication date: 19 December 2011

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

Full work available at URL: https://arxiv.org/abs/1103.3939

zbMATH Keywords

symmetric groupscharacter degreescharacter tables

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Representations of finite symmetric groups (20C30) Arithmetic and combinatorial problems involving abstract finite groups (20D60)

Related Items (14)

Huppert's conjecture for alternating groups ⋮ Complex group algebras of almost simple unitary groups ⋮ Complex group algebras of the direct product of non-isomorphic Suzuki groups ⋮ Characterization of \(\mathrm{PGL}(2, p^2)\) by order and some irreducible character degrees ⋮ Recognition of \(M \times M\) by its complex group algebra where \(M\) is a simple \(K_3\)-group ⋮ Recognition of PSL(2,p) ×PSL(2,p) by its complex group algebra ⋮ Simple exceptional groups of Lie type are determined by their character degrees. ⋮ Unnamed Item ⋮ Complex group algebras of almost simple groups with socle PSL_n(q) ⋮ The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups ⋮ Simple classical groups of Lie type are determined by their character degrees. ⋮ Dimensions of the irreducible representations of the symmetric and alternating group ⋮ Some Extensions of PSL(2,p²) are Uniquely Determined by Their Complex Group Algebras ⋮ A new characterization for the simple group PSL(2, p 2) by order and some character degrees

Uses Software

• GAP

Cites Work

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• PRIME POWER DEGREE REPRESENTATIONS OF THE SYMMETRIC AND ALTERNATING GROUPS
• Verifying Huppert's Conjecture for PSL₃(q) and PSU₃(q²)
• Almost irreducible tensor squares
• A Dual Version of Huppert's  -  Conjecture
• On finite groups and their characters

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