Algebraic and topological properties of Riordan groups over finite fields

In this paper, we investigate algebraic and topological properties of the Riordan groups over finite fields. These groups provide a new class of topologically finitely generated profinite groups with finite width. We also introduce, characterize index-subgroups of our Riordan groups, and finally we...

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Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Gi-Sang Cheon, Chung, Nhan-Phu, Minh-Nhat Phung
Format: Article
Language:English
Subjects:
Algebra
Fields (mathematics)
Subgroups
Topology
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Summary:In this paper, we investigate algebraic and topological properties of the Riordan groups over finite fields. These groups provide a new class of topologically finitely generated profinite groups with finite width. We also introduce, characterize index-subgroups of our Riordan groups, and finally we show exactly the range of Hausdorff dimensions of these groups. The latter results are analogous to the work of Barnea and Klopsch for the Nottingham groups.
ISSN:2331-8422