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, Külshammer, and Sambale. In particular, we determine possible defect groups for blocks with Loewy length 4.
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Sambale, B. Exponent and p-rank of finite p-groups and applications. Arch. Math. 103, 11–20 (2014). https://doi.org/10.1007/s00013-014-0665-x
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DOI: https://doi.org/10.1007/s00013-014-0665-x