Geodesic
Groups of oscillating intermediate growth
Martin Kassabov1 ; Igor Pak2
1 Mathematics, University of Southampton, Southampton SO17 1BG<br/> United Kingdom, and<br/> Department of Mathematics<br/>Cornell University<br/> Ithaca, NY 14853-4201
2 Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, CA 90095-1555
Annals of mathematics, Tome 177 (2013) no. 3, pp. 1113-1145 Cet article a éte moissonné depuis la source Annals of Mathematics website

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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 $e^{n^\alpha}$ 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.

DOI : 10.4007/annals.2013.177.3.7

Martin Kassabov 1 ; Igor Pak 2

1 Mathematics, University of Southampton, Southampton SO17 1BG<br/> United Kingdom, and<br/> Department of Mathematics<br/>Cornell University<br/> Ithaca, NY 14853-4201
2 Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, CA 90095-1555 
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Martin Kassabov; Igor Pak. Groups of oscillating intermediate growth. Annals of mathematics, Tome 177 (2013) no. 3, pp. 1113-1145. doi: 10.4007/annals.2013.177.3.7

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