Archiv der Mathematik

, Volume 103, Issue 1, pp 11–20 | Cite as

Exponent and p-rank of finite p-groups and applications



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.

Mathematics Subject Classification

20D15 20C20 


Exponent p-rank Loewy length 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Institut für MathematikFriedrich-Schiller-UniversitätJenaGermany

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