SSGP topologies on free groups of infinite rank
General Topology
2019-02-05 v1 Functional Analysis
Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1902.00840,
title = {SSGP topologies on free groups of infinite rank},
author = {Dmitri Shakhmatov and Víctor Hugo Yañez},
journal= {arXiv preprint arXiv:1902.00840},
year = {2019}
}