无限秩自由群上的SSGP拓扑
SSGP topologies on free groups of infinite rank
摘要：
证明了每个具有无穷多个生成元的自由群G都有一个Hausdorff群拓扑T，T具有如下性质：对G的单位元的每个T-开邻域U，G中的每个元素g都可以表示为乘积g= g_1g_2. g_k，使得由每个g_i生成的循环群包含在U中.特别地，G允许一个Hausdorff群拓扑具有Gould的小子群生成性质。这提供了一个积极的答案，舒适和古尔德的问题的情况下，自由群无限多个发电机。具有多个生成元的自由群的情况仍然是开放的。
英文摘要：
We prove that every free group G with infinitely many generators admits a Hausdorff group topology T with the following property: for every T-open neighbourhood U of the identity of G, each element g in G can be represented as a product g=g_1 g_2 ... g_k such that the cyclic group generated by each g_i is contained in U. In particular, G admits a Hausdorff group topology with the small subgroup generating property of Gould. This provides a positive answer to a question of Comfort and Gould in the case of free groups with infinitely many generators. The case of free groups with finitely many generators remains open.
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。
