Induced modules of support τ-tilting modules and extending modules of semibricks over blocks of finite groups

In this article we study support tau-tilting modules, semibricks and more over blocks of group algebras. Let kbe an algebraically closed field of characteristic p > 0, (G) over tilde a finite group and Ga normal subgroup of (G) over tilde. Moreover, let (B) over tilde be a block of k (G) over tilde and Ba block of kG covered by (B) over tilde. We show that, under certain conditions for the factor group (G) over tilde /G and B, induced modules and extending modules of support tau-tilting modules and semibricks over Bare also the ones over (B) over tilde, respectively. (c) 2023 Elsevier Inc. All rights reserved.