Gabriela Olteanu

Rational Group Algebras of Finite Groups: From Idempotents to Units of Integral Group Rings

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 of finite nilpotent groups. As an application, we obtain that the unit group of the integral group ring

Finite group algebras of nilpotent groups: A complete set of orthogonal primitive idempotents

{\mathbb Z} G

Computing the Wedderburn decomposition of group algebras by the Brauer–Witt theorem

of a finite nilpotent group G has a subgroup of finite index that is generated by three nilpotent groups for which we have an explicit description of their generators. Another application is a new construction of free subgroups in the unit group. In all the constructions dealt with, pairs of subgroups (H, K), called strong Shoda pairs, and explicit constructed central elements e(G, H, K) play a crucial role. For arbitrary finite groups we prove that the primitive central idempotents of the rational group algebras are rational linear combinations of such e(G, H, K), with (H, K) strong Shoda pairs in subgroups of G.

Construction of minimal non-abelian left group codes

We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group algebra of a nilpotent group.

Rickart and Dual Rickart Objects in Abelian Categories: Transfer via Functors

We present an alternative constructive proof of the Brauer-Witt theorem using the so-called strongly monomial characters that gives rise to an algorithm for computing the Wedderburn decomposition of semisimple group algebras of finite groups.

Strongly Rickart objects in abelian categories

Algorithms to construct minimal left group codes are provided. These are based on results describing a complete set of orthogonal primitive idempotents in each Wedderburn component of a semisimple finite group algebra

An algorithm to compute the Wedderburn decomposition of semisimple group algebras implemented in the GAP package wedderga

{\mathbb F}G

Group rings of finite strongly monomial groups: Central units and primitive idempotents☆

FG for a large class of groups