Prof. Dan Segal

MA, MSc, PhD, DSc

Status

Emeritus

Senior Research Fellow emeritus, All Souls College

+44 1865 279379

Contact form

ORCID iD

https://orcid.org/0000-0002-1882-5866

Research groups

Algebra

Address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Major / recent publications

Algorithms determining finite simple images of finitely presented groups (with M. R. Bridson, D. M. Evans, and M. W. Liebeck)
Invent. Math. 218 (2019), pages 623–648.

On normal subgroups of compact groups (with N. Nikolov), J. Eur. Math. Soc. 16 (2014), 597–618.

Generators and commutators in finite groups; abstract quotients of compact groups (with N. Nikolov), Invent. Math. 190 (2012), 513-602; http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s0…

Words: notes on verbal width in groups
LMS Lect. Notes 361, CUP, 2009. ISBN 978-0-521-74766-0

Polycyclic groups
Cambridge Tracts in Math. 82, CUP, Cambridge, 1983; paperback 2005. ISBN 978-0-521-02394-8

Subgroup growth (with A. Lubotzky)
Progress in Math. 212, Birkhauser, Basel, 2003. ISBN 3-7643-6989-2

Analytic pro-p groups, 2nd ed. (with J.D. Dixon, M.P.F. du Sautoy and A. Mann)
Cambridge Studies in Advanced Mathematics 61, CUP, Cambridge 1999; paperback 2003. ISBN 978-0-521-54218-0

New horizons in pro-p groups (editor, with M. P. F. du Sautoy and A. Shalev)
Progress in Math. 184, Birkhauser, Boston 2000. ISBN 0-8176-4171-8, 3-7643-4171-8

Highlighted publications

Generators and commutators in finite groups; abstract quotients of compact groups

Segal, D Nikolov, N Inventiones Mathematicae volume 190 issue 3 513-602 (15 Nov 2012)

Finitely generated groups with polynomial index growth

Segal, D Pyber, L J. reine angewandte Math. volume 612 173-211 (2007)

On finitely generated profinite groups, I: strong completeness and uniform bounds

Nikolov, N Segal, D ANNALS OF MATHEMATICS volume 165 issue 1 171-238 (2007) https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=elements_prod_1&SrcAuth=WosAPI&KeyUT=WOS:000246342000005&DestLinkType=FullRecord&DestApp=WOS_CPL

On the integer solutions of quadratic equations

Segal, D F.J Grunewald Journal für die reine und angewandte Mathematik (Crelles Journal) volume 569 13-45 (Mar 2004)

The finite images of finitely generated groups.

Segal, D Proceedings of the London Mathematical Society volume 82 issue 3 597-613 (May 2001)

Finitely generated groups of polynomial subgroup growth

Lubotzky, A Mann, A Segal, D Israel Journal of Mathematics volume 82 issue 1-3 363-371 (01 Jun 1993)

DECIDABLE PROPERTIES OF POLYCYCLIC GROUPS

SEGAL, D PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY volume 61 497-528 (1990) https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=elements_prod_1&SrcAuth=WosAPI&KeyUT=WOS:A1990EJ11900004&DestLinkType=FullRecord&DestApp=WOS_CPL

SUBGROUPS OF FINITE INDEX IN NILPOTENT GROUPS

GRUNEWALD, F SEGAL, D SMITH, G INVENTIONES MATHEMATICAE volume 93 issue 1 185-223 (1988) https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=elements_prod_1&SrcAuth=WosAPI&KeyUT=WOS:A1988N924800008&DestLinkType=FullRecord&DestApp=WOS_CPL

Research interests

Algebra, number theory

Prizes, awards, and scholarships

Adams Prize 1981, Whitehead Prize 1985, Ferran Sunyer i Balaguer Prize 2002, Polya Prize 2012

Highlighted books

Words Segal, D (16 Jul 2009)

Subgroup Growth Lubotzky, A Segal, D (2003)

Analytic Pro-P Groups Dixon, J Du Sautoy, M Mann, A Segal, D (26 Aug 1999)

Polycyclic groups Segal, D (1983)

Recent publications

On some relatively free pro-p groups

Segal, D (07 May 2025) http://arxiv.org/abs/2505.04816v1

A profinite analogue of Lasserre's theorem

Segal, D Journal of Algebra volume 629 109-123 (Sep 2023)

On the finite axiomatizability of some metabelian profinite groups

Segal, D (26 Mar 2023) http://arxiv.org/abs/2303.14776v1

Commensurability and bi-interpretability of groups

Segal, D (29 Jan 2023) http://arxiv.org/abs/2301.12506v1

A profinite analogue of Lasserre's theorem

Segal, D (17 Sep 2022) http://arxiv.org/abs/2209.08279v2

Defining R and G(R)

Segal, D Tent, K Journal of the European Mathematical Society volume 25 issue 8 3325-3358 (25 Jun 2022)

Constructing uncountably many groups with the same profinite completion

NIKOLOV, N Segal, D New Zealand Journal of Mathematics (18 Dec 2021)

Finite axiomatizability for profinite groups

Nies, A Segal, D Tent, K Proceedings of the London Mathematical Society volume 123 issue 6 597-635 (24 Aug 2021)

Preferred address

All Souls College, Oxford OX1 4AL