We discuss the growth function of a finitely generated cascade and its connection to the growth function of its related semi-direct product (Conjecture 1.9). The results is applied for simpler proof of well-known results in the realm of geometric group theory. We show that the finitely generated cascades on nilpotent groups obey the dichotomy rule (only polynomial and exponential growth are possible).
Some applications of algebraic entropy to the proof of Milnor-Wolf theorem
Dikranjan D.;Freni D.;
2019-01-01
Abstract
We discuss the growth function of a finitely generated cascade and its connection to the growth function of its related semi-direct product (Conjecture 1.9). The results is applied for simpler proof of well-known results in the realm of geometric group theory. We show that the finitely generated cascades on nilpotent groups obey the dichotomy rule (only polynomial and exponential growth are possible).File in questo prodotto:
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(2019)Some application of algebraic entropi to the proof of Milnor-Wolf Theorem.pdf
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(2019) Some applications of algebraic entropy to the proof of Milnor-Wolf theorem.pdf
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