TY - JOUR T1 - On the Group of $p$-Endotrivial $kG$-Modules AU - Huang , Wenlin JO - Communications in Mathematical Research VL - 2 SP - 106 EP - 116 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.02.02 UR - https://global-sci.org/intro/article_detail/cmr/13510.html KW - $p$-endotrivial module, the group of $p$-endotrivial modules, endo-permutation module, Dade group AB -

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 $T_p(G)\cong T_p(H)$ whenever the subgroup $H$ contains a normalizer of a Sylow $p$-subgroup of $G$, in this case, $K(G)\cong K(H)$. We also prove that the group $D_p(G)$ can be embedded into $T_p(G)$ as a subgroup.