某些有限三维矩阵群的增长性
Growth in Some Finite Three-Dimensional Matrix Groups
摘要：
研究了有限三维矩阵群中乘积集的增长性。特别地，我们证明了任意有限域上的$2\times 2$上三角形矩阵群的两个结果：一个利用乘法组合学技巧的积集估计，以及一个利用关联几何的能量估计.能量法给出了更好的定量结果，但仅适用于小集合。我们还证明了海森堡群的一个能量结果。
英文摘要：
We study the growth of product sets in some finite three-dimensional matrix groups. In particular, we prove two results about the group of $2\times 2$ upper triangular matrices over arbitrary finite fields: a product set estimate using techniques from multiplicative combinatorics, and an energy estimate using incidence geometry. The energy method gives better quantitative results, but only applies to small sets. We also prove an energy result for the Heisenberg group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
