The Brauer indecomposability of Scott modules with vertex $Q_{2^n}\times C_{2^m}$

Abstract

We prove that the Scott module whose vertex is isomorphic to a direct product of a generalized quaternion $2$-group and a cyclic $2$-group is Brauer indecomposable. This result generalizes similar results which are obtained for abelian, dihedral, generalized quaternion, semidihedral and wreathed $2$-group vertices.