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We give an explicit and character-free construction of a complete set of orthogonal primitive idempotents of a rational group algebra of a finite nilpotent group and a full description of the Wedderburn decomposition of such algebras. An immediate consequence is a well-known result of Roquette on the Schur indices of the simple components of group algebras(More)
In 1992 Drinfeld posed the question of finding the set-theoretic solutions of the Yang-Baxter equation. Recently, Gateva-Ivanova and Van den Bergh and Etingof, Schedler and Soloviev have shown a group-theoretical interpretation of involutive non-degenerate solutions. Namely, there is a oneto-one correspondence between involutive non-degenerate solutions on(More)
We classify the finite groups G such that the group of units of the integral group ring ZG has a subgroup of finite index which is a direct product of free-by-free groups. The investigations on the unit group ZG∗ of the integral group ring ZG of a finite group G have a long history and go back to work of Higman [11]. One of the fundamental problems that(More)