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arXiv · 1902.00840

SSGP topologies on free groups of infinite rank

Dmitri Shakhmatov·Víctor Hugo Yañez
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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.

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Dmitri Shakhmatov, Víctor Hugo Yañez. 2019-02-03. SSGP topologies on free groups of infinite rank. https://arxiv.org/abs/1902.00840

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