Group Algebra Extensions of Depth One∗

A ring extension A ⊆ B is said to have depth one if B is isomorphic to a direct summand of An as an (A,A)-bimodule, for some positive integer n. We prove group-theoretic characterizations of this property in the case kH ⊆ kG where H is a subgroup of a finite group G and k is a field. Moreover, we determine when the source algebra of a block of kG with defect group P is a depth one extension of kP