Abstract
We study the Loewy structure of the centralizer algebra k P Q for P a p-group with subgroup Q and k a field of characteristic p. Here k P Q is a special type of Hecke algebra. The main tool we employ is the decomposition k P Q = k C P ( Q ) ⋉ I of k P Q as a split extension of a nilpotent ideal I by the group algebra k C P ( 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 k P Q . 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 k P Q .
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