# Defect of subnormality in modular group algebras

Let $$p$$ be a prime number, $$G$$ a finite p-Group and $$K$$ a finite field with $$\operatorname{char}(K)=p$$. It is well-known that the group $$1+\operatorname{rad}(KG)$$ is a p-group containing $$G$$. $$G$$ is normal in $$1+\operatorname{rad}(KG)$$ if and only if $$G$$ is abelian. As $$1+\operatorname{rad}(KG)$$ is nilpotent, the group $$G$$ is subnormal in $$1+\operatorname{rad}(KG)$$. Is the defect of subnormality known for $$G$$ in $$1+\operatorname{rad}(KG)$$?