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).
@article{1598,
title = {Notes on the Isomorphism and Splitting Problems for Commutative Modular Group Algebras},
journal = {CUBO, A Mathematical Journal},
volume = {9},
year = {2007},
language = {en},
url = {http://dml.mathdoc.fr/item/1598}
}
Danchev, Peter. Notes on the Isomorphism and Splitting Problems for Commutative Modular Group Algebras. CUBO, A Mathematical Journal, Tome 9 (2007) . http://gdmltest.u-ga.fr/item/1598/