Year: 2015
Type: article
Abstract: When considering the unit group of [Formula: see text] ([Formula: see text] the ring of integers of an abelian number field [Formula: see text] and a finite group [Formula: see text]) certain components in the Wedderburn decomposition of [Formula: see text] cause problems for known generic constructions of units; these components are called exceptional. Exceptional components are divided into two types: type 1 is division rings, type 2 is [Formula: see text]-matrix rings. For exceptional components of type 1 we provide infinite classes of division rings by describing the seven cases of minimal groups (with respect to quotients) having those division rings in their Wedderburn decomposition over [Formula: see text]. We also classify the exceptional components of type 2 appearing in group algebras of a finite group over number fields [Formula: see text] by describing all 58 finite groups [Formula: see text] having a faithful exceptional Wedderburn component of this type in [Formula: see text].
Authors: Andreas Bächle, Mauricio Caicedo, Inneke Van Gelder
Institution: Vrije Universiteit Brussel
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1562478191