Brauer indecomposability of Scott modules with semidihedral vertex

Abstract We present a sufficient condition for the $kG$ -Scott module with vertex $P$ to remain indecomposable under Brauer construction any subgroup $Q$ of as $k[Q\,C_G(Q)]$ -module, where $k$ is field characteristic $2$ , and semidihedral -subgroup finite group $G$ . This generalizes results cases abelian or dihedral. The indecomposability defined by R. Kessar, N. Kunugi Mitsuhashi. motivation this paper fact that $p$ -permutation bimodule (where prime) one key steps in order obtain splendid stable equivalence Morita type making use gluing method due Broué, Rickard, Linckelmann Rouquier, then can possibly be lifted derived (splendid Morita) equivalence.