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MR2216706 20F65 (20E08 37F20 37F50)
Bux, Kai-Uwe; Pérez, Rodrigo On the growth of iterated monodromy groups. Topological and asymptotic aspects of group theory, 61–76, Contemp. Math., 394, Amer. Math. Soc., Providence, RI, 2006.
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