The Algebraic Structure of Finite Metabelian Group Algebras

Abstract

An algorithm for the explicit computation of a complete set of primitive central idempotents, Wedderburn decomposition, and the automorphism group of the semisimple group algebra of a finite metabelian group is developed. The algorithm is illustrated with its application to the semisimple group algebra of an arbitrary metacyclic group, and certain indecomposable groups whose central quotient is the Klein four-group.

Key Words:

• Automorphism group
• Finite semisimple group algebra
• Metabelian group
• Primitive central idempotent
• Wedderburn decomposition

2010 Mathematics Subject Classification:

• 16S34
• 20C05
• 16K20

Notes

Communicated by S. Sehgal.