List of Publications

Research Articles

2000-2004 (10)

• Liftings of the elementary group over associative rings, Glasg. Math. J. 42 (2000), 201-209.
  
  
• Automorphisms of the Nottingham group, J. Algebra 223 (2000), 37-56.
  
  
• Normal subgroups in substitution groups of formal power series, J. Algebra 228 (2000), 91-106.
  
  
• Linear bounds for the degree of subgroup growth in terms of the Hirsch length, Bull. London Math. Soc. 32 (2000), 403-408.
  
  
• Zeta functions related to the pro-p group SL ₁¹ (Δ_p), Math. Proc. Camb. Philos. Soc. 135 (2003), 45-57.
  
  
• Pro-p groups with linear subgroup growth, Math. Z. 245 (2003), 335-370; read-only final version: SharedIt version.
  
  
• Index-subgroups of the Nottingham group, joint work with Yiftach Barnea, Adv. Math. 180 (2003), 187-221.
  
  
• How long does it take to generate a group?, joint work with Vsevolod Lev, J. Algebra 261 (2003), 145-171; preprint version: arXiv preprint.
  
  
• Enumerating finite groups without abelian composition factors, Israel J. Math. 137 (2003), 265-284; read-only final version: SharedIt version.
  
  
• Enumerating highly non-soluble groups, in: Finite groups 2003, 219-227, Walter de Gruyter, Berlin, 2004.

2005-2009   (7)

• On the Lie theory of p-adic analytic groups, Math. Z. 249 (2005), 713-730; read-only final version: SharedIt version.
  
  
• Groups with less than n subgroups of index n, Math. Ann. 333 (2005), 67-85; read-only final version: SharedIt version.
  
  
• Analytic groups over general pro-p domains, joint work with Andrei Jaikin-Zapirain, J. London Math. Soc 76 (2007), 365-383.
  
  
• Generating abelian groups by addition only, joint work with Vsevolod Lev, Forum Math. 21 (2009), 23-41; preprint version: arXiv preprint.
  
  
• Zeta functions of three-dimensional p-adic Lie algebras, joint work with Christopher Voll, Math. Z. 263 (2009), 195-210; preprint version: arXiv preprint; read-only final version: SharedIt version.
  
  
• Igusa-type functions associated to finite formed spaces and their functional equations , joint work with Christopher Voll, Trans. Amer. Math. Soc. 361 (2009), 4405-4436; preprint version: arXiv preprint.
  
  
• Analytic pro-p groups of small dimensions, joint work with Jon Gonzalez-Sanchez, J. Group Theory 12 (2009), 711-734; preprint version: arXiv preprint.

2010-2014 (11)

• Automorphism groups of cyclic codes, joint work with Rolf Bienert, J. Algebraic Combin. 31 (2010), 33-52; preprint version: arXiv preprint; read-only final version: SharedIt version.
  
  
• On representation zeta functions of groups and a conjecture of Larsen-Lubotzky, joint work with Nir Avni, Uri Onn, Christopher Voll, C. R. Math. Acad. Sci. Paris 348 (2010), 363-367; extended English preprint version: arXiv preprint.
  
  
• On w-maximal groups, joint work with Jon Gonzalez-Sanchez, J. Algebra 328 (2011), 155-166; preprint version: arXiv preprint.
  
  
• Pro-p groups with constant generating number on open subgroups, joint work with Ilir Snopce, J. Algebra 331 (2011), 263-270; preprint version: arXiv preprint.
  
  
• On the rank of compact p-adic Lie groups, Arch. Math. (Basel) 96 (2011), 321-333; preprint version: arXiv preprint; read-only final version: SharedIt version.
  
  
• Representation zeta functions of some compact p-adic analytic groups, joint work with Nir Avni, Uri Onn, Christopher Voll, in Zeta Functions in Algebra and Geometry, Contemporary Mathematics 566, Amer. Math. Soc., Providence, RI, 2012, 295-330; preprint version: arXiv preprint.
  
  
• Representation zeta functions of compact p-adic analytic groups and arithmetic groups, joint work with Nir Avni, Uri Onn, Christopher Voll, Duke Math. J. 162 (2013), 111-197; preprint version: arXiv preprint.
  
  
• Deformations and rigidity of lattices in solvable Lie groups, joint work with Oliver Baues, J. Topol. 6 (2013), 823-856; preprint version: arXiv preprint.
  
  
• A generalization of the Burnside basis theorem, joint work with Paul Apisa, J. Algebra 400 (2014), 8-16; preprint version: arXiv preprint.
  
  
• The representation zeta function of a FAb compact p-adic Lie group vanishes at -2, joint work with Andrei Jaikin-Zapirain, Jon Gonzalez-Sanchez, Bull. London Math. Soc. 46 (2014), 239-244; preprint version: arXiv preprint.
  
  
• A characterisation of uniform pro-p groups, joint work with Ilir Snopce, Q. J. Math. 65 (2014), 1277-1291; preprint version: arXiv preprint.
  
  

2015-2019 (12)

• A nilpotent group without local functional equations for pro-isomorphic subgroups, joint work with Mark Berman, J. Group Theory 18 (2015), 489-510; preprint version: arXiv preprint.
  
  
• Similarity classes of integral p-adic matrices and representation zeta functions of groups of type A₂ , joint work with Nir Avni, Uri Onn, Christopher Voll, Proc. London Math. Soc. 112 (2016), 267-350; preprint version: arXiv preprint.
  
  
• Arithmetic groups, base change and representation growth, joint work with Nir Avni, Uri Onn, Christopher Voll, Geom. Funct. Anal. (GAFA) 26 (2016), 67-135; preprint version: arXiv preprint.
  
  
• Maximal subgroups of multi-edge spinal groups, joint work with Theofanis Alexoudas, Anitha Thillaisundaram, Groups Geom. Dyn. 10 (2016), 619-648; preprint version: arXiv preprint.
  
  
• The Magnus property for direct products, joint work with Benno Kuckuck, Arch. Math. (Basel) 107 (2016), 379-388; preprint version: arXiv preprint; read-only final version: SharedIt version.
  
  
• Embedding properties of hereditarily just infinite profinite wreath products, joint work with Matteo Vannacci, J. Algebra 476 (2017), 297-310; preprint version: arXiv preprint.
  
  
• The lower rank of direct products of hereditarily just infinite groups, joint work with Matteo Vannacci, Glasg. Math. J. 60 (2018), 225-230; preprint version: arXiv preprint.
  
  
• Maximal subgroups and irreducible representations of generalised multi-edge spinal groups, joint work with Anitha Thillaisundaram, Proc. Edinb. Math. Soc. 61 (2018), 673-703; preprint version: arXiv preprint.
  
  
• A family of class-2 nilpotent groups, their automorphisms and pro-isomorphic zeta functions, joint work with Mark Berman, Uri Onn, Math. Z. 290 (2018), 909-935; preprint version: arXiv preprint; read-only final version: SharedIt version.
  
  
• Hausdorff dimensions in p-adic analytic groups, joint work with Anitha Thillaisundaram, Amaia Zugadi-Reizabal, Israel J. Math. 231 (2019), 1-23; preprint version: arXiv preprint; read-only final version: SharedIt version.
  
  
• Zeta functions associated to admissible representations of compact p-adic Lie groups, joint work with Steffen Kionke, Trans. Amer. Math. Soc. 372 (2019), 7677-7733; preprint version: arXiv preprint.
  
  
• A pro-p group with infinite normal Hausdorff spectra, joint work with Anitha Thillaisundaram, Pac. J. Math. 303 (2019), 569-603; preprint version: arXiv preprint.
  
  

since 2020

• Pro-p groups of positive rank gradient and Hausdorff dimension, joint work with Oihana Garaialde Ocaña, Alejandra Garrido, J. London Math.Soc. 101 (2020), 1008-1040; published version; preprint version: arXiv preprint.
  
  
• Strong conciseness in profinite groups, joint work with Eloisa Detomi, Pavel Shumyatsky, J. London Math. Soc. 102 (2020), 977-993; published open-access version; preprint version: arXiv preprint.
  
  
• Generating pairs of projective special linear groups that fail to lift, joint work with Jan Boschheidgen, Anitha Thillaisundaram, Math. Nachr. 293 (2020), 1251-1258; published open-access version; preprint version: arXiv preprint.
  
  
• A pro-p group with full normal Hausdorff spectra, joint work with Iker de las Heras; Math. Nachr. 295 (2022), 89-102; published open-access version; preprint version: arXiv preprint.
  
  
• Pólya-Carlson dichotomy for coincidence Reidemeister zeta functions via profinite completions, joint work with Alexander Fel'shtyn, Indag. Math. (N.S.) 33 (2022), 753-767; published open-archive version; preprint version: arXiv preprint.
  
  
• Free polynilpotent groups and the Magnus property, joint work with Luis Mendonça, Jan Moritz Petschick; Forum Math. 35 (2023), 573-590; published version; preprint version: arXiv preprint.
  
  
• The structure of groups with all proper quotients virtually nilpotent, joint work with Martyn Quick, Pac. J. Math. 325 (2023), 147-189; published open-access version; preprint version: arXiv preprint.
  
  
• The degree of commutativity of wreath products with infinite cyclic top group, joint work with Iker de las Heras, Andoni Zozaya; Eur. J. Math. 10 (2024), Paper No. 25, 28 pp.; published open-access version; preprint version: arXiv preprint.
  
  
• Finite axiomatizability of the rank and the dimension of a pro-π group, joint work with Martina Conte; Pac. J. Math. 328 (2024), 255-273; published open-access version; preprint version: arXiv preprint.
  
  
• On pro-isomorphic zeta functions of D^*-groups of even Hirsch length, joint work with Mark Berman, Uri Onn, to appear in Israel J. Math.; preprint version: arXiv preprint.
  
  
• The lower p-series of analytic pro-p groups and Hausdorff dimension, joint work with Iker de las Heras and Anitha Thillaisundaram; preprint version: arXiv preprint.

Books and Book Chapters

• Lectures on Profinite Topics in Group Theory, with Nikolay Nikolov and Christopher Voll (edited by Dan Segal), London Mathematical Society Student Texts 77, Cambridge University Press, ISBN 978-0-521-18301-7, February 2011, [basic information at CUP].
  
  
• Abstract quotients of profinite groups, after Nikolov and Segal, Chapter 5 in: New Directions in Locally Compact Groups, edited by Pierre-Emmanuel Caprace and Ncolas Monod, London Mathematical Society Lecture Note Series 447, Cambridge University Press, ISBN 978-1-108-41312-1, February 2018, [basic information at CUP].
  
  

Reports and Surveys

• Zetafunktionen in der Gruppentheorie - mit Augenmerk auf p-adische Liegruppen, in: Mathematisches Institut, Seminars (Y. Tschinkel, ed.), Universität Göttingen, 2004, 65-74. [short survey based on a seminar talk in Göttingen] [PDF-file]
  
  
• Representation zeta functions of compact p-adic Lie groups, in: Profinite and Asymptotic Group Theory, Oberwolfach Reports No. 28/2008 [summary of a conference talk] [Oberwolfach Reports, Volume 5, 2008]
  
  
• Representation growth and representation zeta functions of groups, Note Mat. 33 (2013), 107-120; preprint version: arXiv preprint.
  
  
• Abstract quotients of profinite groups, after Nikolov and Segal, in: Arbeitsgemeinschaft: Totally Disconnected Groups, Oberwolfach Reports No. 47/2014 [summary of an Arbeitsgemeinschaft talk] [Oberwolfach Reports, Volume 11, 2014].
  
  
• Abstract quotients of profinite groups, after Nikolov and Segal (expanded account), preprint version: arXiv preprint.

Theses

• Lifting Problems in General Linear Groups over Residue Class Rings, M.Sc. Thesis, University of East Anglia, 1996.
  
  
• Substitution Groups, Subgroup Growth and Other Topics, D.Phil. Thesis, University of Oxford, 1999. [Abstract in PDF-format]
  
  
• Pro-p Gruppen: Analytische Strukturen und spezielle Fragen zum Untergruppenwachstum, schriftliche Habilitationsleistung, Universität Düsseldorf, 2006.

Other Texts (Lecture Notes etc.)

• Five lectures on analytic pro-p groups, Royal Holloway, University of London, 2007. [Lecture notes for an LMS-EPSRC Short Course on Asymptotic Methods in Infinite Group Theory at Oxford University in September 2007] [PDF-file]
  
  
• Applications of field theory, Royal Holloway, University of London, 2008. [Lecture notes] [PDF-file] [Additional supporting material] [available through moodle guest login]
  
  
• Elementare Zahlentheorie, Düsseldorf, 2005. [Notes from a course in elementary number theory, covering unique factorization in the context of ideals and the theory of quadratic fields] [PDF-file]
  
  
• Endliche Körper - eine kurze Wiederholung, Düsseldorf, 2001. [A short summary of the basic properties of finite fields] [PDF-file]
  
  
• Audio CDs und Reed-Solomon Codes, Düsseldorf, 2001. [Applications of Reed-Solomon Codes in the customary Audio Compact Disc System] [PDF-file]
  
  
• Primzahlen und die Riemannsche Vermutung, Folien zu einem allgemeinverständlichen Vortrag, Tag der Forschung 2005 an der Heinrich-Heine-Universität Düsseldorf. [A public lecture on prime numbers and the Riemann Hypothesis] [PDF-file (German)] [PDF-file (English Translation)]
  
  
• Kubische Gleichungen als Brutkasten komplexer Zahlen, Folien zu einem allgemeinverständlichen Vortrag, Tag der Forschung 2006 an der Heinrich-Heine-Universität Düsseldorf. [A public lecture on cubic equations and complex numbers] [PDF-file]
  
  
• Computational Mathematics I, Royal Holloway, University of London, 2007-08. [Lecture notes and other supporting material] [available through moodle guest login]
  
  
• Computation and Numerical Analysis, Royal Holloway, University of London, 2008. [Supporting material] [available through moodle guest login]
  
  
• Mathematics under the Leaning Tower, Royal Holloway, University of London, 2009. [Slides for an interactive school talk on the harmonic series] [PDF-file]
  
  
• Pi meets Mandelbrot, Royal Holloway, University of London, 2009. [Slides for an interactive school talk on the Mandelbrot set] [PDF-file; deutsche Version für Mathematik Vernetzen 2009 in Düsseldorf: PDF-Datei]