Comptes Rendus
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

Christopher Voll1
1 School of Mathematics, University of Southampton, University Road, Southampton SO17 1BJ, UK
Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1347-1350.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.10.024
Christopher Voll 1

1 School of Mathematics, University of Southampton, University Road, Southampton SO17 1BJ, UK 
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Christopher Voll. Enumerating finite class-2-nilpotent groups on 2 generators. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1347-1350. doi : 10.1016/j.crma.2009.10.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.024/

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

[3] E.A. O'Brien 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] C. Voll Normal subgroup growth in free class-2-nilpotent groups, Math. Ann., Volume 332 (2005), pp. 67-79

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