Abstract:By studying homogeneous polynomials related togroups

the complex index of finite groups is defined.The theory of complexindex and its complex representation has been developed and perfected quicklySo people began to consider the representation of finite fields

that is

modular representation theoryThe basic problem of modular representation theoryfor finite groups is to determine the Morita equivalence class of pblockalgebras of a given finite groupAt present

the international research on modelrepresentation mainly focuses on the following two issues:One is tocharacterize the structure of pblock algebras of known groups

especiallyfinite simple groupsThe other is the qualitative study of pblock algebras ofgeneral finite groupsThe deficient group plays a key role in the block theoryof modular representation theory of finite groups It is the most importantobject connecting the properties of group theory and representation theory Inthis paper

we study the existence of zero deficient blocks of finite groupsByusing the properties of subgroups

the necessary and sufficient conditions forthe existence of null deficient blocks in finite groups are given