On indecomposable Abelian codes and their vertices

Indecomposable nonsemisimple Abelian codes are investigated. The author describes all indecomposable Abelian group codes and shows that the minimal distance of such a code M is the product of the minimal distance of a semisimple Abelian group code and the minimal distance of the source module of M. It is illustrated that the minimal distance of every indecomposable Abelian code depends upon its associated vertex