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Profinite groups with soluble centralisers

Shumyatsky, Pavel LU and Thillaisundaram, Anitha LU (2025) In Monatshefte fur Mathematik 206(4). p.957-966
Abstract

We show that a profinite group, in which the centralisers of non-trivial elements are metabelian, is either virtually pro-p or virtually soluble of derived length at most 4. We furthermore show that a prosoluble group, in which the centralisers of non-trivial elements are soluble of bounded derived length, is either soluble or virtually pro-p.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Primary 20E18, Profinite groups, Soluble centralisers
in
Monatshefte fur Mathematik
volume
206
issue
4
pages
957 - 966
publisher
Springer
external identifiers
  • scopus:85204589118
ISSN
0026-9255
DOI
10.1007/s00605-024-02014-5
language
English
LU publication?
yes
id
b121c5c0-a004-4865-974a-19c6b43080a2
date added to LUP
2024-12-02 11:39:02
date last changed
2025-10-14 10:25:31
@article{b121c5c0-a004-4865-974a-19c6b43080a2,
  abstract     = {{<p>We show that a profinite group, in which the centralisers of non-trivial elements are metabelian, is either virtually pro-p or virtually soluble of derived length at most 4. We furthermore show that a prosoluble group, in which the centralisers of non-trivial elements are soluble of bounded derived length, is either soluble or virtually pro-p.</p>}},
  author       = {{Shumyatsky, Pavel and Thillaisundaram, Anitha}},
  issn         = {{0026-9255}},
  keywords     = {{Primary 20E18; Profinite groups; Soluble centralisers}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{957--966}},
  publisher    = {{Springer}},
  series       = {{Monatshefte fur Mathematik}},
  title        = {{Profinite groups with soluble centralisers}},
  url          = {{http://dx.doi.org/10.1007/s00605-024-02014-5}},
  doi          = {{10.1007/s00605-024-02014-5}},
  volume       = {{206}},
  year         = {{2025}},
}