@article{PMIHES_2000__92__63_0, author = {Du Sautoy, Marcus}, title = {Counting $p$-groups and nilpotent groups}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {63--112}, publisher = {Institut des Hautes \'Etudes Scientifiques}, volume = {92}, year = {2000}, mrnumber = {1839487}, zbl = {01656529}, language = {en}, url = {http://www.numdam.org/item/PMIHES_2000__92__63_0/} }
Du Sautoy, Marcus. Counting $p$-groups and nilpotent groups. Publications Mathématiques de l'IHÉS, Volume 92 (2000), pp. 63-112. http://www.numdam.org/item/PMIHES_2000__92__63_0/
[1] On a special class of p-groups, Acta Math. 100 (1958), 49-92. | MR | Zbl
,[2] Algebraic groups of automorphisms of nilpotent groups and Lie algebras, J. London Math. Soc. 33 (1986), 453-466. | MR | Zbl
and ,[3] The rationality of the Poincaré series associated to the p-adic points on a variety, Invent. Math. 77 (1984), 1-23. | MR | Zbl
,[4] p-adic and real subanalytic sets, Annals of Math. 128 (1988), 79-138. | MR | Zbl
and ,[5] Motivic Igusa zeta functions, J. Algebraic Geom., 7 (1998), 505-537. | MR | Zbl
and ,[6] Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math., 135 (1999), 201-232. | MR | Zbl
and ,[7] Analytic pro-p groups, Second Edition, Cambridge Studies in Advanced Mathematics, 61, Cambridge, CUP, 1999. | MR | Zbl
, , and ,[8] Finitely generated groups, p-adic analytic groups and Poincaré series, Annals of Math. 137 (1993), 639-670. | MR | Zbl
,[9] Zeta functions and counting finite p-groups, Electronic Research Announcements of the American Math. Soc., 5 (1999), 112-122. | MR | Zbl
,[10] A nilpotent group and its elliptic curve : non-uniformity of local zeta functions of groups, MPI preprint 2000-2085. To appear in Israel J. of Math. 126. | Zbl
,[11] Counting subgroups in nilpotent groups and points on elliptic curves, MPI preprint 2000-2086.
,[12] Natural boundaries for zeta functions of groups, preprint.
,[13] Analytic properties of Euler products of Igusa-type zeta functions and subgroup growth of nilpotent groups, C. R. Acad. Sci. Paris 329, Série 1 (1999), 351-356. | MR | Zbl
and ,[14] Analytic properties of zeta functions and subgroup growth, Annals of Math. 152 (2000), 793-833. | MR | Zbl
and ,[15] Uniformity for 2-generator free nilpotent groups, in preparation.
and ,[16] Motivic zeta functions of infinite dimensional Lie algebras, École polytechnique, preprint series 2000-2012.
and ,[17] Functional equations and uniformity for local zeta functions of nilpotent groups, Amer. J. Math. 118 (1996), 39-90. | MR | Zbl
and ,[18] Zeta functions of crystallographic groups and analytic continuation, Proc. London Math. Soc. 79 (1999), 511-534. | MR | Zbl
, and ,[19] Zeta functions of groups, in New horizons in pro-p groups. Progress in Mathematics, vol. 184 (ed M. P. F. du Sautoy, D. Segal and A. Shalev), p. 249-286. Boston, Birkhäuser (2000). | MR | Zbl
and ,[20] Field Arithmetic, Springer-Verlag, Berlin, Heidelberg, New York, 1986. | MR | Zbl
and ,[21] Subgroups of finite index in nilpotent groups, Invent. Math. 93 (1988), 185-223. | MR | Zbl
, and ,[22] Enumerating p-groups, I, Proc. London Math. Soc. 10 (1960), 24-30. | MR | Zbl
,[23] Enumerating p-groups, II, Proc. London Math. Soc. 10 (1960), 566-582. | MR | Zbl
,[24] A classical introduction to modern number theory, Second Edition, Graduate texts in mathematics 84, Springer-Verlag, New York, Berlin, Heidelberg, 1993.
and ,[25] Algebra, Addison-Wesley, Reading, MA, 1965. | MR | Zbl
,[26] On p-groups of maximal class II, Quart. J. Math. Oxford (2) 29 (1978), 175-186. | MR | Zbl
and ,[27] On p-groups of maximal class III, Quart. J. Math. Oxford (2) 29 (1978), 281-299. | MR | Zbl
and ,[28] Space groups and groups of prime-power order I, Arch. Math. (Basel) 35 (1980), 193-202. | MR | Zbl
and ,[29] The structure of finite p-groups, J. London Math. Soc. 50 (1994), 49-67. | MR | Zbl
,[30] Combinatorial Group Theory, Wiley, Chichester, UK, 1966.
, and ,[31] Groups of prime-power order, Groups-Canberra 1989, Lecture Notes in Math., 1456 Springer-Verlag (1990), 49-62. | MR | Zbl
,[32] Classifying 2-groups by coclass, Trans. Amer. Math. Soc. 351 (1999), 131-169. | MR | Zbl
and ,[33] The problem of strong approximation and the Kneser-Tits conjecture for algebraic groups, Math. USSR-Izv. 3 (1969), 1139-1147. | Zbl
,[34] Addendum, Math. USSR-Izv. 4 (1970), 784-786. | Zbl
,[35] Algebraic Groups and Number Theory, Pure and Applied Mathematics 139, London, Academic Press, 1994. | MR | Zbl
and ,[36] Polycyclic Groups, Cambridge tracts in mathematics, 82, CUP (1983). | MR | Zbl
,[37] The structure of finite p-groups : effective proof of the coclass conjectures, Invent. Math. 115 (1994), 315-345. | MR | Zbl
,[38] Enumerating p-groups, Proc. London Math. Soc. 15 (1965), 151-166. | MR | Zbl
,[39] Enumerative Combinatorics, vol. 1, Cambridge Studies in Advanced Mathematics, 49, CUP, 1997. | Zbl
,