On the Group of ρ-endotrivial κG-modules

In this paper, we define a group T_ρ(G) of p-endotrivial κG-modules and a generalized Dade group D_ρ(G) for a finite group G. We prove that T_ρ(G)? T_ρ(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 D_ρ(G) can be embedded into T_ρ(G) as a subgroup.