In this paper we investigate gradings on tame blocks of group algebras whose defect group is dihedral. We classify gradings on an arbitrary dihedral block up to graded Morita equivalence. We do this by computing the group of outer automorphisms that fix the isomorphism classes of simple modules. We also show how to grade these blocks via transfer of gradings via dervied equivalences.

A connection of lattice of quasi-antiorders of set with apartness with the direct square of lattice of coequalities of set with apartness is obtained. AMS Mathematics Subject Classification (2000): Primary: 03F65, Secondary: 06B99

In this paper we give another isomorphism theorem on anti-ordered semigroups. Mathematics Subject Classification: Primary: 03F65; Secondary: 20M10

. In this paper we show that tame blocks of group algebras with quaternion defect groups and three isomorphism classes of simple modules can be non-trivially graded. We prove this by using the transfer of gradings via derived equivalences.