Algebraic and topological properties of Riordan groups over finite fields

TL;DR

This paper explores the algebraic and topological structure of Riordan groups over finite fields, revealing their properties as topologically finitely generated profinite groups with finite width, and characterizing their subgroups and Hausdorff dimensions.

Contribution

It introduces and characterizes Riordan groups over finite fields as a new class of topologically finitely generated profinite groups with finite width, extending existing group theory results.

Findings

Riordan groups over finite fields are topologically finitely generated profinite groups

Characterization of index-subgroups of these Riordan groups

Determination of the range of Hausdorff dimensions for these groups

Abstract

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.