Modular centralizer algebras corresponding to p-groups

We study the Loewy structure of the centralizer algebra kPQ for P a p-group with subgroup Q and k a field of characteristic p. Here kPQ is a special type of Hecke algebra. The main tool we employ is the decomposition kPQ=kCP(Q)⋉I of kPQ as a split extension of a nilpotent ideal I by the group algebra kCP(Q). We compute the Loewy structure for several classes of groups, investigate the symmetry of the Loewy series, and give upper and lower bounds on the Loewy length of kPQ. Several of these results were discovered through the use of MAGMA, especially the general pattern for most of our computations. As a final application of the decomposition, we determine the representation type of kPQ.