Groups of oscillating intermediate growth | Annals of Mathematics

Abstract We construct an uncountable family of finitely generated groups of intermediate growth, with growth functions of new type. These functions can have large oscillations between lower and upper bounds, both of which come from a wide class of functions. In particular, we can have growth oscillating between enα and any prescribed function, growing as rapidly as desired. Our construction is built on top of any of the Grigorchuk groups of intermediate growth and is a variation on the limit of permutational wreath product.

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数学年刊(Annals of Mathematics)

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