The pro-p group of upper unitriangular matrices

Mazza, Nadia (2017) The pro-p group of upper unitriangular matrices. Journal of Pure and Applied Algebra, 221 (12). pp. 2928-2952. ISSN 0022-4049

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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.

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Journal Article
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Journal of Pure and Applied Algebra
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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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Deposited On:
24 Feb 2017 09:04
Last Modified:
08 May 2021 03:25