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The lower p-series of analytic pro-p groups and Hausdorff dimension

Heras, Iker de las ; Klopsch, Benjamin LU and Thillaisundaram, Anitha LU (2025) In Journal of the London Mathematical Society 112(2).
Abstract

Let (Formula presented.) be a (Formula presented.) -adic analytic pro- (Formula presented.) group of dimension (Formula presented.), with lower (Formula presented.) -series (Formula presented.). We produce an approximate series which descends regularly in strata and whose terms deviate from (Formula presented.) in a uniformly bounded way. This brings to light a new set of rational invariants (Formula presented.), canonically associated to (Formula presented.), such that (Formula presented.) and such that the Hausdorff dimensions (Formula presented.) of closed subgroups (Formula presented.) with respect to (Formula presented.) are confined to the set (Formula presented.) In particular, the Hausdorff spectrum (Formula presented.) is... (More)

Let (Formula presented.) be a (Formula presented.) -adic analytic pro- (Formula presented.) group of dimension (Formula presented.), with lower (Formula presented.) -series (Formula presented.). We produce an approximate series which descends regularly in strata and whose terms deviate from (Formula presented.) in a uniformly bounded way. This brings to light a new set of rational invariants (Formula presented.), canonically associated to (Formula presented.), such that (Formula presented.) and such that the Hausdorff dimensions (Formula presented.) of closed subgroups (Formula presented.) with respect to (Formula presented.) are confined to the set (Formula presented.) In particular, the Hausdorff spectrum (Formula presented.) is discrete and consists of at most (Formula presented.) rational numbers.

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Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of the London Mathematical Society
volume
112
issue
2
article number
e70271
publisher
John Wiley & Sons Inc.
external identifiers
  • scopus:105014117280
ISSN
0024-6107
DOI
10.1112/jlms.70271
language
English
LU publication?
yes
id
b5136a5a-42b3-46c7-955b-54142abe5a8c
date added to LUP
2025-11-07 10:45:23
date last changed
2025-11-07 10:46:15
@article{b5136a5a-42b3-46c7-955b-54142abe5a8c,
  abstract     = {{<p>Let (Formula presented.) be a (Formula presented.) -adic analytic pro- (Formula presented.) group of dimension (Formula presented.), with lower (Formula presented.) -series (Formula presented.). We produce an approximate series which descends regularly in strata and whose terms deviate from (Formula presented.) in a uniformly bounded way. This brings to light a new set of rational invariants (Formula presented.), canonically associated to (Formula presented.), such that (Formula presented.) and such that the Hausdorff dimensions (Formula presented.) of closed subgroups (Formula presented.) with respect to (Formula presented.) are confined to the set (Formula presented.) In particular, the Hausdorff spectrum (Formula presented.) is discrete and consists of at most (Formula presented.) rational numbers.</p>}},
  author       = {{Heras, Iker de las and Klopsch, Benjamin and Thillaisundaram, Anitha}},
  issn         = {{0024-6107}},
  language     = {{eng}},
  number       = {{2}},
  publisher    = {{John Wiley & Sons Inc.}},
  series       = {{Journal of the London Mathematical Society}},
  title        = {{The lower p-series of analytic pro-p groups and Hausdorff dimension}},
  url          = {{http://dx.doi.org/10.1112/jlms.70271}},
  doi          = {{10.1112/jlms.70271}},
  volume       = {{112}},
  year         = {{2025}},
}