On the Group of p-endotrivial kG-modules

In this paper,we define a group Tp(G) of p-endotrivial kG-modules and a generalized Dade group Dp(G) for a finite group G.We prove that Tp(G) ≌ Tp(H) whenever the subgroup H contains a normalizer of a Sylow p-subgroup of G,in this case,K(G) ≌ K(H).We also prove that the group Dp(G) can be embedded into Tp(G) as a subgroup.