A Modular Version of Maschke′s Theorem for Groups with Cyclic p-Sylow Subgroups Original Research Article

We prove that the group algebra of a finite group with a cyclic p-Sylow subgroup over an algebraically closed field is a specialization of a parameter-dependent multiplication structure which gives a semisimple algebra for general values of the parameter. We actually prove the existence of such a specialization for any block of cyclic defect group.