Abstract
We review some known results and open problems related to the growth of groups. For a finitely generated group Γ, given whenever necessarytogether with a finite generating set, we discuss the notions of
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(1)
uniformly exponential growth,
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(2)
growth tightness,
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(3)
regularity of growth series,
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(4)
classical growth series (with respect to word lengths),
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(5)
growth series with respect to weights,
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(6)
complete growth series,
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(7)
spectral radius of simple random walks on Cayley graphs.
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The first author acknowledges support from the Foundation National Suisse de la Recherche Scientifique, from the Russian Foundation for Fundamental Research, Grant 96-01-00974, and from INTAS, Grant 94-3420.
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Grigorchuk, R., De La Harpe, P. On problems related to growth, entropy, and spectrum in group theory. Journal of Dynamical and Control Systems 3, 51–89 (1997). https://doi.org/10.1007/BF02471762
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DOI: https://doi.org/10.1007/BF02471762