Complex group algebras of almost simple unitary groups. Issue 5 (3rd May 2020)

• Record Type: Journal Article
• Authors: Shirjian, Farrokh; Iranmanesh, Ali; Shafiei, Farideh
• Is Part Of: Communications in algebra. Volume 48:Issue 5(2020)
• Page Start: 1919
• Page End: 1940
• Publication Date: 2020-05-03
• Subjects: Almost simple groups -- character degrees -- complex group algebras -- finite reductive groups; Primary 20C33 -- 20C15 -- 20G40; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1710162
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: The aim of this article is to contribute to a question of R. Brauer that "when do non-isomorphic groups have isomorphic complex group algebras?" Let H and G be finite groups where PSU n ( q ) ≤ G ≤ PGU n ( q ), and let X 1 ( H ) denote the first column of the complex character table of H . In this article, we show that if X 1 ( H ) = X 1 ( G ), then H ≅ G provided that q + 1 divides neither n nor n – 1. Consequently, it is shown that G is uniquely determined by the structure of its complex group algebra. This in particular extends a recent result of Bessenrodt et al. [ Algebra Number Theory 9 (2015), 601–628] to the almost simple groups of arbitrary rank.