Growth in higher Baumslag–Solitar groups

Ayla P. Sánchez; Michael Shapiro

doi:10.1007/s10711-017-0277-2

Growth in higher Baumslag–Solitar groups

Ayla P. Sánchez, Michael Shapiro

Department of Life Sciences

Wheaton College

Research output: Contribution to journal › Article › peer-review

3 Citations (SciVal)

Abstract

We study the HNN extension of (Formula presented.) given by the cubing endomorphism (Formula presented.), and prove that such groups have rational growth with respect to the standard generating sets. We compute the subgroup growth series of the horocyclic subgroup (Formula presented.) in this family of examples, prove that for each m the subgroup has rational growth. We then use the tree-like structure of these groups to see how to compute the growth of the whole group.

Original language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Geometriae Dedicata
Early online date	12 Aug 2017
DOIs	https://doi.org/10.1007/s10711-017-0277-2
Publication status	E-pub ahead of print - 12 Aug 2017

Keywords

Baumslag–Solitar groups
Growth
Rationality
Solvable groups

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-017-0277-2

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abstract = "We study the HNN extension of (Formula presented.) given by the cubing endomorphism (Formula presented.), and prove that such groups have rational growth with respect to the standard generating sets. We compute the subgroup growth series of the horocyclic subgroup (Formula presented.) in this family of examples, prove that for each m the subgroup has rational growth. We then use the tree-like structure of these groups to see how to compute the growth of the whole group.",

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AU - Shapiro, Michael

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N2 - We study the HNN extension of (Formula presented.) given by the cubing endomorphism (Formula presented.), and prove that such groups have rational growth with respect to the standard generating sets. We compute the subgroup growth series of the horocyclic subgroup (Formula presented.) in this family of examples, prove that for each m the subgroup has rational growth. We then use the tree-like structure of these groups to see how to compute the growth of the whole group.

AB - We study the HNN extension of (Formula presented.) given by the cubing endomorphism (Formula presented.), and prove that such groups have rational growth with respect to the standard generating sets. We compute the subgroup growth series of the horocyclic subgroup (Formula presented.) in this family of examples, prove that for each m the subgroup has rational growth. We then use the tree-like structure of these groups to see how to compute the growth of the whole group.

KW - Baumslag–Solitar groups

KW - Growth

KW - Rationality

KW - Solvable groups

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UR - http://dx.doi.org/10.1007/s10711-017-0277-2

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JF - Geometriae Dedicata

ER -

Growth in higher Baumslag–Solitar groups

Abstract

Keywords

ASJC Scopus subject areas

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