右序群和鲍姆slag - 索利塔群中的小加倍问题 - II
On Small Doubling in Right-Ordered Groups and Baumslag-Solitar Groups-II
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中文总结 AI 辅助
本文在右序群中进一步研究满足|S²| = 3|S| - 3的非空子集S的结构，还对鲍姆slag - 索利塔群BS(1, q)（q≠ - 1）中满足该条件且单位元为S最小值的非空有限子集S进行完整刻画。
中文摘要 AI 辅助
最近，莫汉等人[《结果数学》80 (2025)，第4期，122]在某些限制下回答了右序群中弗赖曼的3k - 4猜想。本文进一步研究满足小加倍条件|S²| = 3|S| - 3的右序群的非空子集S的结构。此外，我们还对鲍姆slag - 索利塔群BS(1, q)（q∈Z且q≠ - 1）中所有满足|S²| = 3|S| - 3且单位元是S的最小值的非空有限子集S进行了完整刻画。
英文摘要
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 $\mathrm{BS}(1,q)$ (with $q \in \mathbb{Z}$ and $q \neq -1$) for which $|S^2| = 3|S|-3$ and the identity element is the minimum of $S$.
发表机构
- School of Engineering and Technology, Vivekananda Institute of Professional Studies-Technical Campus（维韦卡南达专业研究学院技术校区工程学院与技术学院）
- Department of Mathematical and Computational Sciences, National Institute of Technology Surathkal（苏拉特卡尔国家理工学院数学与计算科学系）
机构由 AI 辅助整理，请以论文原文为准。
