Notes on the Isomorphism and Splitting Problems for Commutative Modular Group Algebras

Peter Danchev

Notes on the Isomorphism and Splitting Problems for Commutative Modular Group Algebras

Authors

Peter Danchev General Kutuzov Street, bl. 7, floor 2, apart, 44003 Plovdiv, Bulgaria.

Keywords:

Isomorphism problem, p-splitting groups, p-mixed groups, Warfield groups, simply presented groups

Abstract

It is proved that the p-Splitting Group Basic Problem for arbitrary abelian groups and the Splitting Group Basic Problem for p-mixed groups are, in fact, equivalent in the commutative group algebra of characteristic p. In addition, a new scheme of obtaining the complete set of invariants for such a group algebra of a p-splitting group is given. In particular, as application, the full system of invariants for a group algebra when the group is p-splitting Warfield is established as well. This supplies own recent results in (Bol. Soc. Mat. Maxicana, 2004) and (Acta Math. Sinica, 2005).