Subgroup distortion in wreath products of cyclic groups |
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Authors: | Tara C. Davis Alexander Yu. Olshanskii |
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Affiliation: | a Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN 37240, USAb Department of Algebra, Faculty of Mechanics and Mathematics, Moscow State University, 119899 Moscow, Russia |
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Abstract: | We study the effects of subgroup distortion in the wreath products , where A is finitely generated abelian. We show that every finitely generated subgroup of has distortion function equivalent to some polynomial. Moreover, for A infinite, and for any polynomial lk, there is a 2-generated subgroup of having distortion function equivalent to the given polynomial. Also, a formula for the length of elements in arbitrary wreath product easily shows that the group has distorted subgroups, while the lamplighter group has no distorted (finitely generated) subgroups. In the course of the proof, we introduce a notion of distortion for polynomials. We are able to compute the distortion of any polynomial in one variable over Z,R or C. |
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Keywords: | 20F69 20E22 20E10 20F05 |
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