On blocks of finite groups with central hyperfocal subgroups

Let b be a p-block of a finite group G with a defect group P and a hyperfocal subgroup Q⩽P. Let c be a block of NG(Q) associated with b. We show that if Q⩽Z(P) then the Brauer categories of b and c are equal. We show that if Q is abelian and G is p-solvable, then b and c are Morita equivalent. Moreover we show that if b is the principal block, Q is cyclic and Q⩽Z(P), then b and c are isotypic.