On k(D)-Blocks

摘要

The objective of this research paper is to study numerical relationships between a block of a finite group and a defect group of such block. We define a new notion which is called a strongly k(D)- block and give a necessary and sufficient condition of a block with a cyclic defect group to be a k(D) -block in term of its inertial index. We believe that the notion and the results in this work will contribute to the developments of the theory of blocks of finite groups.