Benjamin Klopsch
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List of Publications


list on MathSciNet list on Zentralblatt MATH preprints on the arXiv

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 11p), 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

  • On pro-isomorphic zeta functions of D*-groups of even Hirsch length, joint work with Mark Berman, Uri Onn, preprint (2015); preprint version: arXiv preprint.

  • Pro-p groups of positive rank gradient and Hausdorff dimension, joint work with Oihana Garaialde Ocaña, Alejandra Garrido, to appear in J. London Math.Soc.; preprint version: arXiv preprint.

  • Strong conciseness in profinite groups, joint work with Eloisa Detomi, Pavel Shumyatsky, to appear in J. London Math. Soc.; 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, to appear in Math. Nachr.; published open-access version; preprint version: arXiv preprint.

  • A pro-p group with full normal Hausdorff spectra, joint work with Iker de las Heras; to appear in Math. Nachr.; 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]


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Last significant update: January 2019