On the depth of subgroups and group algebra extensions

We investigate notions of depth for inclusions of rings B⊆A, in particular for group algebra extensions RH⊆RG for finite groups H⩽G and a non-zero commutative ring R. A group-theoretic (or combinatorial) notion of depth for H in G is defined and used to show that RH⊆RG has always finite depth. We compare the depths of H⩽G and RH⊆RG, and investigate how the depth varies with R.