On perfect isometries and isotypies inalternating groups

Perfect isometries and isotypies are constructed for alternating groups between blocks with abelian defect groups and the Brauer correspondents of these blocks. These perfect isometries and isotypies satisfy additional compatibility conditions which imply that an extended Broué conjecture holds for the principal block of an almost simple group with an abelian Sylow $p$-subgroup and a generalized Fitting subgroup isomorphic to an alternating group.