Abstract
We calculate explicitly the normal zeta function of the free group of class two on four generators, denoted by F2,4. This has Hirsch length ten.
Similar content being viewed by others
References
M. P. F. Sautoy Particledu (2001) ArticleTitleA nilpotent group and its elliptic curve: non-uniformity of local zeta functions of groups Israel J. Math. 126 269–288
M. P. F. Sautoy Particledu (2000) ArticleTitleCounting finite p-groups and nilpotent groups, Inst. Hautes Études Scientifiques Publ. Math. 92 63–112
M. P. F. Sautoy Particledu (2002) ArticleTitleCounting subgroups in nilpotent groups and points on elliptic curves J. Reine. Angew. Math. 549 1–21
du Sautoy, M. P. F.: Zeta Functions of Groups: The Quest for Order Versus the Flight from Ennui, Groups (St Andrews 2001), Volume 1, Oxford, Univ. Press, 2003.
M. P. F. Sautoy Particledu F. J. Grunewald (2000) ArticleTitleAnalytic properties of zeta functions and subgroup growth Ann. of Math. 152 793–833
F. J. Grunewald D. Segal G. C. Smith (1988) ArticleTitleSubgroups of finite index in nilpotent groups Invent. Math. 93 185–223 Occurrence Handle10.1007/BF01393692
J. Harris (1992) Algebraic Geometry: A First Course Springer-Verlag New York
J. W. P. Hirschfeld J. A. Thas (1991) General Galois Geometries Clarendon Press Oxford
Paajanen P. M.: On the degree of polynomial subgroup growth in class 2 nilpotent groups, preprint.
C. Voll (2004) ArticleTitleZeta functions of groups and enumeration in Bruhat-Tits buildings Amer. J. Math. 126 IssueID5 1005–1032
Voll, C.: Functional equations for local normal zeta functions of nilpotent groups, Geom. Funct. Anal. to appear.
Paajanen P. M.: Zeta functions of groups and arithmetic geometry, DPhil Thesis, Oxford, 2005.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Paajanen, P.M. The Normal Zeta Function of the Free Class Two Nilpotent Group on Four Generators. Geom Dedicata 115, 135–162 (2005). https://doi.org/10.1007/s10711-005-3953-6
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10711-005-3953-6