SSGP topologies on free groups of infinite rank
SSGP topologies on free groups of infinite rank
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无限秩自由群上的 SSGP 拓扑
DOI：
10.1016/j.topol.2019.02.043
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发表时间：
2019
影响因子：
0.6
通讯作者：
Yanez Victor Hugo
中科院分区：
文献类型：
--
作者：
Shakhmatov Dmitri;Yanez Victor Hugo
我们证明每一个免费的G组无穷多的发电机承认一群豪斯多夫拓扑T和以下属性:每不开邻居U G的身份,每个元素G∈G可以表示成一个产品G = G 1 G 2…G k, k是一个正整数(取决于G)和每个生成的循环群G我包含在美国特别是G承认一群豪斯多夫拓扑与小的子群生成古尔德的属性。这为具有无穷多个产生子的自由群的Comfort和Gould问题提供了一个肯定的答案。具有有限多个生成器的自由组的情况仍然没有定论。
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∈ G can be represented as a product g= g 1 g 2… g k, where k is a positive integer (depending on g) and 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.