2019年6月1日
SSGP topologies on free groups of infinite rank
Topology and its Applications
- ,
- 巻
- 259
- 号
- 開始ページ
- 384
- 終了ページ
- 410
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.topol.2019.02.043
© 2019 Elsevier B.V. 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.
- リンク情報
- ID情報
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- DOI : 10.1016/j.topol.2019.02.043
- ISSN : 0166-8641
- SCOPUS ID : 85063403109