Abstract
We bound the order of a finite p-group in terms of its exponent and p-rank. Here the p-rank is the maximal rank of an abelian subgroup. These results are applied to defect groups of p-blocks of finite groups with given Loewy length. Doing so, we improve results in a recent paper by Koshitani, Kulshammer, and Sambale. In particular, we determine possible defect groups for blocks with Loewy length 4.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have