Simple Components of the Center of FG/J(FG)

Abstract

Let G be a finite group, F a field, FG the group ring of G over F, and J(FG) the Jacobson radical of FG. Using a result of Berman and Witt, we give a method to determine the structure of the center of FG/J(FG), provided that F satisfies a field theoretical condition.

Key Words:

• Finite groups
• Galois group
• Group rings
• Simple components

2000 Mathematics Subject Classification:

• Primary 16S34
• Secondary 20C05

ACKNOWLEDGMENTS

The author wishes to thank Prof. B. Kulshammer for useful conversations and for calling his attention to Külshammer (1984) and Leonardo Linhares for translating Külshammer (1984) into English. The author is very grateful to Prof. César Polcino Milies for useful comments and suggestions.

This research was partially supported by FAPESP, proc. 2004/15319-3.

Notes

Communicated by M. Ferrero.