On finite -groups minimally of class greater than two
Rolf Brandl
Universität Würzburg, GermanyGabriella Corsi Tani
Firenze, ItalyLuigi Serena
Università degli Studi di Firenze, Italy
![On finite $p$-groups minimally of class greater than two cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rsmup-volume-138.png&w=3840&q=90)
Abstract
Let be a finite nilpotent group of class three whose proper subgroups and proper quotients are nilpotent of class at most two. We show that is either a 2-generated -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 and , . If 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 -groups minimally of class greater than two. Rend. Sem. Mat. Univ. Padova 138 (2017), pp. 129–146
DOI 10.4171/RSMUP/138-7