The Principal P-Block Of Finite Groups With Abelian Sylow 2-Subgroups

LetG be a finite group with an abelian Sylow 2-subgroup, P a Sylow p-subgroup of G and BO(G) the principal block of G. Assuming p≠ 3 and that P is abelian, we prove that BO(G) and BO(NG(P)) are splendidly Rickard equivalent.