The Loewy length of a tensor product of modules of a dihedral two-group

While the finite-dimensional modules of the dihedral 2-groups over fields of characteristic 2 were classified over 30 years ago, very little is known about the tensor products of such modules. In this article, we compute the Loewy length of the tensor product of two modules of a dihedral two-group in characteristic 2. As an immediate consequence, we determine when such a tensor product has a projective direct summand.