(untitled) (Communications in Mathematical Research, 2019)
In this paper, we define a group T_p(G) of p-endotrivial kG-modules and a generalized Dade group D_p(G) for a finite group G. We prove that T_p(G)T_p(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_p(G) can be embedded into T_p(G) as a subgroup.