Geodesic
Degrees of growth of finitely generated groups, and the theory of invariant means
Izvestiya. Mathematics , Tome 25 (1985) no. 2, pp. 259-300

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This paper gives a negative solution to the problem of Milnor concerning the degrees of growth of groups. The construction also answers a question of Day concerning amenable groups. A number of other results are obtained on residually finite finitely generated infinite 2-groups. Bibliography: 51 titles. 
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     title = {Degrees of growth of finitely generated groups, and the theory of invariant means},
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R. I. Grigorchuk. Degrees of growth of finitely generated groups, and the theory of invariant means. Izvestiya. Mathematics , Tome 25 (1985) no. 2, pp. 259-300. http://geodesic.mathdoc.fr/item/IM2_1985_25_2_a1/