On the Blocks of the Centralizer of the G-Fixed Points Subalgebra of the Interior G-Algebra

Abstract

Let OG be a p-modular group algebra and H be a subgroup of G containing the normalizer of a p-subgroup P of G; in Section 2, for an interior G-algebra A, we associate a certain block of with each block of C _A (A ^G ), and for an interior H-algebra B, we associate a certain block of with each block of C _B (B ^H ); we have shown that these associate relationships respect Brauer Correspondence for block algebras and the tensor product of interior G-algebras, we have also characterized further Extended Green Correspondence by these associate relationships. Indeed, we attain on the points with the multiplicity 1 of G-algebras the generalized forms of these associate relationships in Section 1.

Keywords:

• Block
• Centralizer
• G-algebra
• G-associate relationship

2000 Mathematics Subject Classification:

• 20C20

ACKNOWLEDGMENTS

I am grateful to the referee for his/her checking carefully the article, and his/her deep thoughts on the associate relationships for blocks in the first manuscript, indeed, the present version of this article comes mainly from the idea of the referee.

Notes

Communicated by A. Turull.