Complex group algebras of almost simple groups with socle PSLn(q). Issue 2 (1st February 2018)

• Record Type: Journal Article
• Authors: Shirjian, Farrokh; Iranmanesh, Ali
• Is Part Of: Communications in algebra. Volume 46:Issue 2(2018)
• Page Start: 552
• Page End: 573
• Publication Date: 2018-02-01
• Subjects: Almost simple groups -- character degrees -- complex group algebras; 20C15 -- 20C05 -- 20C33; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1324868
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let H be a finite group, n ≥3, and q be a prime power such that q −1 divides neither n nor n −1. Denote by X 1 ( H ) the first column of the ordinary character table of H . Let G be a finite group such that P S L n ( q ) ≤ G ≤ P G L n ( q ) . In this paper, we will show that if X 1 ( H ) = X 1 ( G ), then H ≅ G . As a consequence, we show that the almost simple groups G are uniquely determined by the structure of their complex group algebras. This extends a result of Tong-Viet [30 ] to a family of almost simple groups of Lie type of arbitrary rank.