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Paper   IPM / M / 15884
School of Mathematics
  Title:   Complex group algebras of almost simple unitary groups
  Author(s):  Farideh Shafiei (Joint with F. Shirjian and A. Iranmanesh)
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  48
  Year:  2020
  Pages:   1919-1940
  Supported by:  IPM
he 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 PSUn(q)≤G≤PGUn(q), and let X1(H) denote the first column of the complex character table of H. In this article, we show that if X1(H)=X1(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.

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