Algebras and Representation Theory

, Volume 17, Issue 1, pp 305–320 | Cite as

Characterizing Finite Quasisimple Groups by Their Complex Group Algebras

Article

Abstract

A finite group L is said to be quasisimple if L is perfect and L/Z(L) is nonabelian simple, in which case we also say that L is a cover of L/Z(L). It has been proved recently (Nguyen, Israel J Math, 2013) that a quasisimple classical group L is uniquely determined up to isomorphism by the structure of \({{\mathbb C}} L\), the complex group algebra of L, when L/Z(L) is not isomorphic to PSL3(4) or PSU4(3). In this paper, we establish the similar result for these two open cases and also for covers with nontrivial center of simple groups of exceptional Lie type and sporadic groups. Together with the main results of Tong-Viet (Monatsh Math 166(3–4):559–577, 2012, Algebr Represent Theor 15:379–389, 2012), we obtain that every quasisimple group except covers of the alternating groups is uniquely determined up to isomorphism by the structure of its complex group algebra.

Keywords

Complex group algebras Quasisimple groups Exceptional groups Groups of Lie type Sporadic groups 

Mathematics Subject Classifications (2010)

Primary 20C33 20C15 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsThe University of AkronAkronUSA
  2. 2.School of Mathematics, Statistics and Computer ScienceUniversity of KwaZulu-NatalPietermaritzburgSouth Africa

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