The Existence of pblocks of Defect 0 in a Finite Groups with Some Subgroups Being Seminormal

Abstract

By studying homogeneous polynomials related to groups, the complex index of finite groups is defined.The theory of complex index and its complex representation has been developed and perfected quickly So people began to consider the representation of finite fields, that is, modular representation theoryThe basic problem of modular representation theory for finite groups is to determine the Morita equivalence class of pblock algebras of a given finite groupAt present, the international research on model representation mainly focuses on the following two issues:One is to characterize the structure of pblock algebras of known groups, especially finite simple groupsThe other is the qualitative study of pblock algebras of general finite groupsThe deficient group plays a key role in the block theory of modular representation theory of finite groups It is the most important object connecting the properties of group theory and representation theory In this paper, we study the existence of zero deficient blocks of finite groupsBy using the properties of subgroups, the necessary and sufficient conditions for the existence of null deficient blocks in finite groups are given

Keywords

• nilpotent group
• pblock of defect 0
• defect group
• semi normal subgroups