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 
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     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/}
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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/

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