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Bibliography
M. Atiyah and I. MacDonald, Commutative Algebra, Addison-Wesley, Reading Massachusetts.
H. Bass, The degree of polynomial growth of finitely generated groups, Proc. London Math. Soc. (3) 25 (1972), 603–614.
N. Bourbaki, Groupes et algebres de Lie, Chapters 4, 5 et 6. Paris, Hermann, 1968.
A. Borel, Sur la cohomologie des espaces fibres princepaux et des espaces homogenes de groupes de Lie compacts, Annals of Math., 57 (1956), 115–207.
M.R. Bott, An application of the Morse theory to the topology of Lie groups, Bull. Soc. Math. France, 84 (1956), 251–281.
J. Cannon, The growth of the closed surface groups and compact hyperbolic Coxeter groups (preprint).
J. Cannon, The combinatorial structure of co-compact discrete hyperbolic groups, (preprint).
P. Cartier, Les arrangements d'hyperplans: un chapitre de geometrie combinatoire. Sem. Bourbaki 1980/81, no. 561.
C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math., 77 (1955), 778–782.
A.J. Coleman, The Betti numbers of the simple groups, Can. J. Math. 10 (1958), 349–356.
H.S.M. Coxeter, The product of generators of a finite group generated by reflections, Duke Math. Jour., 43 (1951), 765–782.
H.S.M. Coxeter and W.O. Moser, Generators and relators for discrete groups, New York, Springer.
A. Durfee, Fourteen characterizations of rational double points and simple critical points.
D. Gromov, Groups of polynomial growth and expanding maps, I.H.E.S., 1980 (preprint).
M. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of Hecke rings of p-adic Chevalley groups, Publ. Math. Inst. Hautes Et. Sci., 25 (1965), 5–48.
J. Milnor, A note on curvature and the fundamental group, J. Diff. Geometry, 2 (1968), 1–7.
J. Milnor, Growth of finitely generated solvable groups, J. Diff. Geometry, 2 (1968), 447–449.
P. Orlik and L. Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), 167–189.
P. Orlik and L. Solomon, Unitary reflection groups and cohomology, Inv. Math., 59 (1980), 77–94.
G. Polya and Szego, Aufgaben und lehrsatze aus der analysis II, Berlin, Springer, 1925.
R. Salem, Power series with integer coefficients, Duke Math. J., 12 (1945), 153–172.
J.P. Serre, Cohomologie des groupes discrets, in Prospects in Mathematics, Princeton, Princeton University Press, (1971), 77–169 (esp. p. 112 remark and p. 145 prop/ 26(d)).
L. Solomon, The orders of the finite Chevalley groups, J. of Algebra, 3 (1966), 376–393.
R. Steinberg, Finite reflection groups, Trans. Amer. Math. Soc., 91 (1959), 493–504.
A.S. Svarc, A volume invariant of coverings, Dokl. Akad. Nauk SSSR, 105 (1953), 32–34.
H. Terao, Generalized exponents of a free arrangement of hyperplanes and Shepherd-Todd-Brieskorn formula, Invent. Math.
J. Tits, Groupes a croissance polynomiale, Sem. Bourbaki, 1980/81, no. 572.
P. Wagreich, Growth functions of discrete groups in dimension 2, to appear.
J.A. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Diff. Geometry, 2 (1968), 421–446.
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Wagreich, P. (1982). The growth function of a discrete group. In: Carrell, J.B. (eds) Group Actions and Vector Fields. Lecture Notes in Mathematics, vol 956. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101514
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DOI: https://doi.org/10.1007/BFb0101514
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