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    Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Pure and Applied Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Pure and Applied Algebra, 221, 12, 2017 DOI: 10.1016/j.ijleo.2017.02.063

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The pro-p group of upper unitriangular matrices

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>12/2017
<mark>Journal</mark>Journal of Pure and Applied Algebra
Issue number12
Volume221
Number of pages25
Pages (from-to)2928-2952
Publication statusPublished
Early online date23/02/17
Original languageEnglish

Abstract

Abstract We study the pro-p group G whose finite quotients give the prototypical Sylow p-subgroup of the general linear groups over a finite field of prime characteristic p. In this article, we extend the known results on the subgroup structure of G. In particular, we give an explicit embedding of the Nottingham group as a subgroup and show that it is selfnormalising. Holubowski ([13–15]) studies a free product C p ⁎ C p as a (discrete) subgroup of G and we prove that its closure is selfnormalising of infinite index in the subgroup of 2-periodic elements of G. We also discuss change of rings: field extensions and a variant for the p-adic integers, this latter linking G with some well known p-adic analytic groups. Finally, we calculate the Hausdorff dimensions of some closed subgroups of G and show that the Hausdorff spectrum of G is the whole interval [ 0 , 1 ] which is obtained by considering partition subgroups only.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Journal of Pure and Applied Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Pure and Applied Algebra, 221, 12, 2017 DOI: 10.1016/j.ijleo.2017.02.063