On k(D)-Blocks

Ahmad M. Alghamdi^*

Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Alqura University, Makkah, Saudi Arabia.

DOI: 10.4236/apm.2015.54018                

Abstract

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.

Keywords

Brauer’s k(B) Problem, Blocks with Cyclic Defect Groups

Conflicts of Interest

The authors declare no conflicts of interest.

References

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