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|Paper IPM / M / 15884||
he aim of this article is to contribute to a question of R. Brauer that âwhen do non-isomorphic groups have isomorphic complex group algebras?â Let H and G be finite groups where PSUn(q)â¤Gâ¤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 Hâ
G provided that q + 1 divides neither n nor n â 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), 601â628] to the almost simple groups of arbitrary rank.
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