Reduction theorem for support $\tau$-tilting modules over group algebras

In studying the structure of derived categories of module categories of group algebras or their blocks, it is fundamental to classify support $\tau$-tilting modules. Koshio and Kozakai showed that the structure of support $\tau$-tilting modules over blocks of finite groups can be reduced to that of their subgroups under suitable conditions. We show that the 'quotient reduction' is also valid under suitable conditions.