no. 23-24
Group Theory
Enumerating finite class-2-nilpotent groups on 2 generators
[Énumération des groupes nilpotents de classe 2 engendrés par 2 générateurs]
Présenté par : Jean-Pierre Serre
Voll, Christopher1
1 School of Mathematics, University of Southampton, University Road, Southampton SO17 1BJ, UK
Comptes Rendus. Mathématique, Tome 347 (2009) no. 23-24, pp. 1347-1350

We compute the numbers g(n,2,2) of nilpotent groups of order n, of class at most 2 generated by at most 2 generators, by giving an explicit formula for the Dirichlet generating function ∑n=1∞g(n,2,2)n−s.

On calcule les nombres g(n,2,2) de groupes nilpotents d'ordre n, de classe au plus 2, engendrés par au plus 2 générateurs, en donnant une formule explicite pour la fonction génératrice de Dirichlet ∑n=1∞g(n,2,2)n−s.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.10.024

Voll, Christopher 1

1 School of Mathematics, University of Southampton, University Road, Southampton SO17 1BJ, UK 
@article{CRMATH_2009__347_23-24_1347_0,
     author = {Voll, Christopher},
     title = {Enumerating finite class-2-nilpotent groups on 2 generators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1347--1350},
     year = {2009},
     publisher = {Elsevier},
     volume = {347},
     number = {23-24},
     doi = {10.1016/j.crma.2009.10.024},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.crma.2009.10.024/}
}
TY  - JOUR
AU  - Voll, Christopher
TI  - Enumerating finite class-2-nilpotent groups on 2 generators
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 1347
EP  - 1350
VL  - 347
IS  - 23-24
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.crma.2009.10.024/
DO  - 10.1016/j.crma.2009.10.024
LA  - en
ID  - CRMATH_2009__347_23-24_1347_0
ER  - 
%0 Journal Article
%A Voll, Christopher
%T Enumerating finite class-2-nilpotent groups on 2 generators
%J Comptes Rendus. Mathématique
%D 2009
%P 1347-1350
%V 347
%N 23-24
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.crma.2009.10.024/
%R 10.1016/j.crma.2009.10.024
%G en
%F CRMATH_2009__347_23-24_1347_0
Voll, Christopher. Enumerating finite class-2-nilpotent groups on 2 generators. Comptes Rendus. Mathématique, Tome 347 (2009) no. 23-24, pp. 1347-1350. doi: 10.1016/j.crma.2009.10.024

[1] du Sautoy, M.P.F. Counting p-groups and nilpotent groups, Publ. Math. I.H.E.S., Volume 92 (2000), pp. 63-112

[2] Grunewald, F.J.; Segal, D.; Smith, G.C. Subgroups of finite index in nilpotent groups, Invent. Math., Volume 93 (1988), pp. 185-223

[3] O'Brien, E.A. The p-group generation algorithm, J. Symbolic Comput., Volume 9 (1990) no. 5–6, pp. 677-698 (Computational group theory, Part 1)

[4] C. Voll, Zeta functions of groups and enumeration in Bruhat–Tits buildings, Ph.D. thesis, University of Cambridge, 2002

[5] Voll, C. Normal subgroup growth in free class-2-nilpotent groups, Math. Ann., Volume 332 (2005), pp. 67-79

Cité par Sources :