Commun. Math. Res., 34 (2018), pp. 106-116.
Published online: 2019-12
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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.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.02.02}, url = {http://global-sci.org/intro/article_detail/cmr/13510.html} }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.