JournalsrsmupVol. 138pp. 129–146

On finite pp-groups minimally of class greater than two

  • Rolf Brandl

    Universität Würzburg, Germany
  • Gabriella Corsi Tani

    Firenze, Italy
  • Luigi Serena

    Università degli Studi di Firenze, Italy
On finite $p$-groups minimally of class greater than two cover
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Abstract

Let GG be a finite nilpotent group of class three whose proper subgroups and proper quotients are nilpotent of class at most two. We show that GG is either a 2-generated pp-group or a 3-generated 3-group. In the first case the groups of maximal order with respect to a given exponent are all isomorphic except in the cases where p=2p=2 and exp(G)=2r\mathrm {exp}(G)= 2^r, r4r\geq 4. If GG is 3-generated, then we show that there is a unique group of maximal order and exponent 3; but a similar result is not valid for exponent 9.

Cite this article

Rolf Brandl, Gabriella Corsi Tani, Luigi Serena, On finite pp-groups minimally of class greater than two. Rend. Sem. Mat. Univ. Padova 138 (2017), pp. 129–146

DOI 10.4171/RSMUP/138-7