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On Small Doubling in Right-Ordered Groups and Baumslag-Solitar Groups-II
Abstract
Recently, Mohan et al. [Results Math. 80 (2025), No. 4, 122] answered Freiman's 3k−4 conjecture in right-ordered groups under certain restrictions. In this paper, we take a step further by investigating the structure of nonempty subsets S of a right-ordered group satisfying the small doubling condition |S2| = 3|S|−3. Moreover, we provide a complete characterization of all nonempty finite subsets S of the Baumslag-Solitar group BS(1,q) (with q ∈ ℤ and q ≠ −1) for which |S2| = 3|S|−3 and the identity element is the minimum of S.
Related
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BibTeX
@misc{mohan2026small,
title = {{On Small Doubling in Right-Ordered Groups and Baumslag-Solitar Groups-II}},
author = {Mohan and Neetu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.11194},
eprint = {2607.11194},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11194},
}
RIS
TY - UNPB
TI - On Small Doubling in Right-Ordered Groups and Baumslag-Solitar Groups-II
AU - Mohan
AU - Neetu
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2607.11194
UR - https://arxiv.org/abs/2607.11194
AB - Recently, Mohan et al. [Results Math. 80 (2025), No. 4, 122] answered Freiman's 3k−4 conjecture in right-ordered groups under certain restrictions. In this paper, we take a step further by investigating the structure of nonempty subsets S of a right-ordered group satisfying the small doubling condition |S^2| = 3|S|−3. Moreover, we provide a complete characterization of all nonempty finite subsets S of the Baumslag-Solitar group BS(1,q) (with q ∈ ℤ and q ≠ −1) for which |S^2| = 3|S|−3 and the identity element is the minimum of S.
ER -