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

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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).

Keywords

Isomorphism problem , p-splitting groups , p-mixed groups , Warfield groups , simply presented groups
  • Peter Danchev General Kutuzov Street, bl. 7, floor 2, apart, 44003 Plovdiv, Bulgaria.
  • Pages: 39–45
  • Date Published: 2007-04-01
  • Vol. 9 No. 1 (2007): CUBO, A Mathematical Journal

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Published

2007-04-01

How to Cite

[1]
P. Danchev, “Notes on the Isomorphism and Splitting Problems for Commutative Modular Group Algebras”, CUBO, vol. 9, no. 1, pp. 39–45, Apr. 2007.

Issue

Vol. 9 No. 1 (2007): CUBO, A Mathematical Journal

Section

Articles