論文

査読有り 招待有り
2019年6月1日

SSGP topologies on free groups of infinite rank

Topology and its Applications
  • Dmitri Shakhmatov
  • ,
  • Víctor Hugo Yañez

259
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
DOI
https://doi.org/10.1016/j.topol.2019.02.043
Scopus
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85063403109&origin=inward
Scopus Citedby
https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85063403109&origin=inward
ID情報
  • DOI : 10.1016/j.topol.2019.02.043
  • ISSN : 0166-8641
  • SCOPUS ID : 85063403109

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