Geodesic
Zeta functions and counting finite p-groups
du Sautoy, Marcus1
1 DPMMS, 16 Mill Lane, Cambridge CB2 1SB, UK
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 112-122.

Voir la notice de l'article provenant de la source American Mathematical Society

We announce proofs of a number of theorems concerning finite $p$-groups and nilpotent groups. These include: (1) the number of $p$-groups of class $c$ on $d$ generators of order $p^n$ satisfies a linear recurrence relation in $n$; (2) for fixed $n$ the number of $p$-groups of order $p^n$ as one varies $p$ is given by counting points on certain varieties mod $p$; (3) an asymptotic formula for the number of finite nilpotent groups of order $n$; (4) the periodicity of trees associated to finite $p$-groups of a fixed coclass (Conjecture P of Newman and O’Brien). The second result offers a new approach to Higman’s PORC conjecture. The results are established using zeta functions associated to infinite groups and the concept of definable $p$-adic integrals.
DOI : 10.1090/S1079-6762-99-00069-4

du Sautoy, Marcus 1

1 DPMMS, 16 Mill Lane, Cambridge CB2 1SB, UK 
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du Sautoy, Marcus. Zeta functions and counting finite p-groups. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 112-122. doi : 10.1090/S1079-6762-99-00069-4. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00069-4/

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