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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)
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)
Let R be a commutative ring, G a group and RG its group ring. Let ϕ σ : RG → RG denote the involution defined by ϕ σ (r g g) = r g σ(g)g −1 , where σ : G → {±1} is a group homo-morphism (called an orientation morphism). An element x in RG is said to be antisymmetric if ϕ σ (x) = −x. We give a full characterization of the groups G and its orientations for(More)
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