Benjamin Klopsch

List of Publications

Research Articles

  • 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 (&Deltap), Math. Proc. Camb. Philos. Soc. 135 (2003), 45-57.

  • Pro-p groups with linear subgroup growth, Math. Z. 245 (2003), 335-370.

  • 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.

  • Enumerating highly non-soluble groups, in: Finite groups 2003, 219-227, Walter de Gruyter GmbH & Co. KG, Berlin, 2004.

  • On the Lie theory of p-adic analytic groups, Math. Z. 249 (2005), 713-730.

  • Groups with less than n subgroups of index n, Math. Ann. 333 (2005), 67-85.

  • 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 versions: Oberwolfach Preprints, OWP 2007 - 10 and arXiv preprint].

  • 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 versions: Max-Planck-Institut für Mathematik Bonn, Preprint Series 2006 (31) and 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].

  • Automorphism groups of cyclic codes, joint work with Rolf Bienert, J. Algebraic Combin. 31 (2010), 33-52,
    [preprint version: arXiv preprint].

  • 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].

  • Representation zeta functions of compact p-adic analytic groups and arithmetic groups, joint work with Nir Avni, Uri Onn, Christopher Voll, preprint (2010),
    [preprint version: arXiv preprint].

  • Representation zeta functions of some compact p-adic analytic groups, joint work with Nir Avni, Uri Onn, Christopher Voll, to appear in: Recent Trends on Zeta Functions in Algebra and Geometry, Contemporary Mathematics series,
    [preprint version: arXiv preprint].

  • Base change and representation growth, joint work with Nir Avni, Uri Onn, Christopher Voll, preprint (2011),
    [preprint version: arXiv preprint].

  • Deformations and rigidity of lattices in solvable Lie groups, joint work with Oliver Baues, preprint (2011),
    [preprint version: arXiv preprint].

  • Representation zeta functions for SL 3, joint work with Nir Avni, Uri Onn, Christopher Voll, in preparation.

Books and Surveys

  • 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 9780521183017, February 2011, [basic information at CUP].

  • Representation Zeta functions of compact p-adic Lie groups, in: Profinite and Asymptotic Group Theory, Oberwolfach Reports No. 28/2008 [A summary of a conference talk] [Oberwolfach Reports]

  • Zetafunktionen in der Gruppentheorie - mit Augenmerk auf p-adische Liegruppen, in: Mathematisches Institut, Seminars (Y. Tschinkel, ed.), Universität Göttingen, 2004, 65-74. [A short survey based on a seminar talk in Göttingen] [PDF-file]

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]

Back to Benjamin' s mathematical panopticon.

Last updated: March 2009