Alternating and sporadic simple groups are determined by their character degrees.

DOI10.1007/s10468-010-9247-1zbMath1252.20005OpenAlexW1999903714MaRDI QIDQ453560

Hung P. Tong-Viet

Publication date: 27 September 2012

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10468-010-9247-1

zbMATH Keywords

sporadic simple groupsfinite simple groupsirreducible complex charactersalternating groupscharacter degreesTits group

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Representations of finite symmetric groups (20C30) Simple groups: sporadic groups (20D08) Representations of sporadic groups (20C34) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (14)

A new characterization for some extensions of \(\mathrm{PSL}(2,q)\) for some \(q\) by some character degrees. ⋮ Huppert's conjecture for alternating groups ⋮ Quasisimple classical groups and their complex group algebras. ⋮ Complex group algebras of almost simple unitary 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. ⋮ Symmetric groups are determined by their character degrees. ⋮ Complex group algebras of almost simple groups with socle PSL_n(q) ⋮ Characterizing finite quasisimple groups by their complex group algebras. ⋮ 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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• On the minimal degrees of characters of \(S_n\)
• Some simple groups which are determined by the set of their character degrees. I
• Some simple groups which are determined by the set of their character degrees. II.
• On finite simple groups of order divisible by three primes only
• SMALLEST DEGREES OF REPRESENTATIONS OF EXCEPTIONAL GROUPS OF LIE TYPE
• PRIME POWER DEGREE REPRESENTATIONS OF THE SYMMETRIC AND ALTERNATING GROUPS
• On the minimal dimensions of irreducible representations of symmetric groups
• Verifying Huppert's Conjecture for PSL₃(q) and PSU₃(q²)
• On the Number of Components of a Graph Related to Character Degrees
• Almost irreducible tensor squares
• The Prime Graph of a Sporadic Simple Group
• Prime power degree representations of quasi-simple groups

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