Direct and Inverse Problems in Baumslag-Solitar Group $BS(1,3)$
| Autor: | Singh, Sandeep, Kaur, Ramandeep |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | For integers $m$ and $n$, the Baumslag-Solitar groups, denoted as $BS(m,n)$, are groups generated by two elements with a single defining relation: $BS(m,n) = \langle a, b | a^mb=ba^n\rangle$. The sum of dilates, denoted as $r \cdot A + s \cdot B$ for integers $r$ and $s$, is defined as $\{ra + sb; a\in A, b\in B\}$. In 2014, Freiman et al. \cite{freiman} derived direct and inverse results for sums of dilates and applied these findings to address specific direct and inverse problems within Baumslag-Solitar groups, assuming suitable small doubling properties. In 2015, Freiman et al. \cite{freiman15} tackled the general problem of small doubling types in a monoid, a subset of the Baumslag-Solitar group $BS(1,2)$. This paper extends these investigations to solve the analogous problem for the Baumslag-Solitar group $BS(1,3)$. Comment: arXiv admin note: text overlap with arXiv:1303.3053 by other authors |
| Databáze: | arXiv |
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