On finite p-groups minimally of class greater than two
Brandl, Rolf1 ; Corsi Tani, Gabriella2 ; Serena, Luigi3
1 Universität Würzburg, Germany
2 Firenze, Italy
3 Università degli Studi di Firenze, Italy
Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 129-146.

Let G be a finite nilpotent group of class three whose proper subgroups and proper quotients are nilpotent of class at most two. We show that G is either a 2-generated p-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=2 and exp (G)=2 r , r≥4. If G 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.

Publié le :
DOI : 10.4171/RSMUP/138-7
Classification : 20
Mots-clés : Finite $p$-groups, varieties of groups, relatively free groups
Brandl, Rolf 1 ; Corsi Tani, Gabriella 2 ; Serena, Luigi 3

1 Universität Würzburg, Germany
2 Firenze, Italy
3 Università degli Studi di Firenze, Italy 
@article{RSMUP_2017__138__129_0,
     author = {Brandl, Rolf and Corsi Tani, Gabriella and Serena, Luigi},
     title = {On finite $p$-groups minimally of class greater than two},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {129--146},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {138},
     year = {2017},
     doi = {10.4171/RSMUP/138-7},
     mrnumber = {3743249},
     zbl = {1404.20013},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/138-7/}
}
TY  - JOUR
AU  - Brandl, Rolf
AU  - Corsi Tani, Gabriella
AU  - Serena, Luigi
TI  - On finite $p$-groups minimally of class greater than two
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2017
SP  - 129
EP  - 146
VL  - 138
PB  - European Mathematical Society Publishing House
PP  - Zuerich, Switzerland
UR  - http://www.numdam.org/articles/10.4171/RSMUP/138-7/
DO  - 10.4171/RSMUP/138-7
ID  - RSMUP_2017__138__129_0
ER  - 
%0 Journal Article
%A Brandl, Rolf
%A Corsi Tani, Gabriella
%A Serena, Luigi
%T On finite $p$-groups minimally of class greater than two
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2017
%P 129-146
%V 138
%I European Mathematical Society Publishing House
%C Zuerich, Switzerland
%U http://www.numdam.org/articles/10.4171/RSMUP/138-7/
%R 10.4171/RSMUP/138-7
%F RSMUP_2017__138__129_0
Brandl, Rolf; Corsi Tani, Gabriella; Serena, Luigi. On finite $p$-groups minimally of class greater than two. Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 129-146. doi : 10.4171/RSMUP/138-7. http://www.numdam.org/articles/10.4171/RSMUP/138-7/

Cité par Sources :