Characterizing finite quasisimple groups by their complex group algebras.

DOI10.1007/s10468-012-9400-0zbMath1303.20001OpenAlexW2091843462MaRDI QIDQ2015184

Hung Ngoc Nguyen, Hung P. Tong-Viet

Publication date: 23 June 2014

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

Full work available at URL: https://doi.org/10.1007/s10468-012-9400-0

zbMATH Keywords

sporadic simple groupsfinite simple groupsfinite groups of Lie typecomplex group algebrasisomorphism problemfinite quasisimple groupsquasisimple classical groupsfinite exceptional groups

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Representations of sporadic groups (20C34) Simple groups: alternating groups and groups of Lie type (20D06) Representations of finite groups of Lie type (20C33)

Related Items (6)

Complex group algebras of almost simple unitary groups ⋮ Complex group algebras of the direct product of non-isomorphic Suzuki groups ⋮ 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 ⋮ Unnamed Item ⋮ Complex group algebras of almost simple groups with socle PSL_n(q)

Uses Software

• GAP

Cites Work

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• On groups with isomorphic complex group algebras
• Simple classical groups of Lie type are determined by their character degrees.
• SMALLEST DEGREES OF REPRESENTATIONS OF EXCEPTIONAL GROUPS OF LIE TYPE
• Character degree graphs that are complete graphs
• The Prime Graph of a Sporadic Simple Group
• Minimal characters of the finite classical groups
• Prime power degree representations of quasi-simple groups

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