Vrije Universiteit Brussel


Andreas Bächle

Personal information

My coordinates

  • Address: Vrije Universiteit Brussel
    DWIS
    Pleinlaan 2
    B-1050 Brussels
    Belgium
  • Office: G.6.322A
  • Phone: +32 2 629 3551
  • E-mail:
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Research

Research interests

  • Group Rings
  • Group Theory
  • Ring Theory
  • Representation Theory
  • Computer Algebra and its Applications

Submitted manuscripts / Preprints (in reverse chronological order)

  1. On the first Zassenhaus conjecture and direct products.
    joint with W. Kimmerle and M. Serrano, submitted, 17 pages, 2018.
    arXiv:1801.09422 [math.RA].

Published and accepted articles (in reverse chronological order)

  1. On the Prime Graph Question for Integral Group Rings of 4-primary groups II.
    joint with L. Margolis.
    Algebras and Representation Theory, in press, 21 pages, 2018.
    Journal | arXiv:1606.01506 [math.RT].
  2. The status of the Zassenhaus conjecture for small groups.
    joint with A. Herman, A. Konovalov, L. Margolis and G. Singh.
    Experimental Mathematics, in press, 6 pages, 2017.
    Journal | arXiv:1609.00042 [math.RA].
  3. Integral group rings of solvable groups with trivial central units.
    Forum Mathematicum 30(4):845-855, 2018.
    Journal | arXiv:1701.04347 [math.GR].
  4. HeLP: A GAP package for torsion units in integral group rings.
    joint with L. Margolis.
    Journal of Software for Algebra and Geometry 8:1-9, 2018.
    Journal | arXiv:1507.08174 [math.RT].
  5. Groups whose elements are not conjugate to their powers.
    joint with B. Sambale.
    Archiv der Mathematik (Basel) 110(5):447-454, 2018.
    Journal | arXiv:1801.05975 [math.GR].
  6. Algorithmic aspects of units in group rings.
    joint with W. Kimmerle and L. Margolis.
    Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, G. Böckle, W. Decker, G. Malle (eds.), Springer Verlag, p. 1-22, 2018.
    Book | arXiv:1612.06171 [math.RT].
  7. On the Prime Graph Question for Integral Group Rings of 4-primary groups I.
    joint with L. Margolis.
    International Journal of Algebra and Computation 27(6), 731-767, 2017.
    Journal | arXiv:1601.05689 [math.RT] | GAP-file referred to in the article.
  8. Rational conjugacy of torsion units in integral group rings of non-solvable groups.
    joint with L. Margolis.
    Proceedings of the Edinburgh Mathematical Society 60(4), 813-830, 2017.
    Journal | arXiv:1305.7419 [math.RT].
  9. On the Prime Graph Question for Almost Simple Groups with an Alternating Socle.
    joint with M. Caicedo.
    International Journal of Algebra and Computation 27(3), 333-347, 2017.
    Journal | arXiv:1510.04598 [math.GR] (arXiv version contains additional example).
  10. The subgroup normalizer problem for integral group rings of some nilpotent and metacyclic groups.
    Communications in Algebra 44(10): 4341-4349, 2016.
    Journal | arXiv:1401.7861 [math.GR].
  11. A classification of exceptional components in group algebras over abelian number fields
    joint with M. Caicedo and I. Van Gelder.
    Journal of Algebra and Its Applications 15(5), 1650092, 32 pages, 2016.
    Journal | arXiv:1412.5458 [math.RT].
  12. A survey on the normalizer problem for integral group rings.
    Groups St Andrews 2013. Campbell, C. M., Quick, M. R., Robertson, E. F. & Roney-Dougal, C. M. (eds.). Cambridge University Press, p. 152-159 (London Mathematical Society Lecture Note Series; vol. 422), 2015.
    Book
  13. Torsion subgroups in the units of the integral group ring of PSL(2,p3).
    joint with L. Margolis.
    Archiv der Mathematik (Basel) 105(1):1-11, 2015.
    Journal | arXiv:1412.7700 [math.GR].
  14. On torsion subgroups in integral group rings of finite group.
    joint with W. Kimmerle.
    Journal of Algebra 326:34-46, 2011.
    Journal | Stuttgarter Mathematische Berichte 2009-005.
Co-authors: Mauricio Caicedo, Allen Herman, Wolfgang Kimmerle, Alexander Konovalov, Leo Margolis, Benjamin Sambale, Mariano Serrano, Gurmail Singh, Inneke Van Gelder.

Selected talks

  • Rationality of groups and integral group rings. Advances in Group Theory and Applications, Lecce, Italy, September 05 - 08, 2017.
  • Rationality of groups and centers of integral group rings. Groups St Andrews, Birmingham, England, August 05 - 13, 2017. Slides.
  • Rationality of groups and centers of integral group rings. Seminar Gruppen und Darstellungen, Kaiserslautern, Germany, May 11, 2017.
  • Rationality of groups and centers of integral group rings. Seminar, Florence, Italy, March 08, 2017.
  • Centers of integral group rings. Oberseminar Algebra, Stuttgart, Germany, February 21, 2017.
  • From Groups to Group Rings -- and back. PhD-seminar (talk for general mathematical audience), Ghent, Belgium, December 12, 2016.
  • On Torsion Units in Integral Group Rings. Seminar, Wuppertal, Germany, July 05, 2016.
  • Torsion Units in Integral Group Rings. Computational Methods for Representations and Group Rings, Stuttgart, Germany, February 18 & 19, 2016. Slides.
  • On Torsion Subgroups in Integral Group Rings of Almost Simple Groups. Groups and their Actions, Będlewo, Poland, June 22-26, 2015. Slides.
  • On the normalizers of subgroups in integral group rings. DMV-PTM Mathematical Meeting, Poznan, Poland, September 17 - 20, 2014. Slides.
  • On the prime graph question for 4-primary groups I. Brock International Conference on Groups, Rings and Group Rings, Brock University, St. Catharines, Canada, July 28 - August 01, 2014. Slides.
  • The HeLP-method: A computational approach to torsion units in group rings. Annual conference of the DFG priority project SPP 1489, Evangelische Akademie Bad Boll, Germany, March 03 - 07, 2014. Slides.
  • Rational conjugacy of torsion units in integral group rings of non-solvable groups. Groups St Andrews, St Andrews, Scotland, July 04 - 10, 2013. Slides.
  • On the normalizer problem for subgroups. Representation Theory Days, Hannover, Germany, November 11 - 12, 2011.
  • On the normalizer property for subgroups. Groups, Rings and Group Rings, Edmonton, Canada, July 11 - 15, 2011. Slides.
  • Torsion subgroups in V(ZG). Arithmetic of Group Rings and Related Objects, Aachen, Germany, March 22 - 26, 2010.
  • On torsion units in ZSz(q). Groups and Hopf Algebras, St. John's, Canada, June 03 - 07, 2009.
  • On torsion units in integral group rings - Torsion elements. Computeralgebra-Tagung, Kassel, Germany, May 14 - 16, 2009.

Misc

  • HeLP - The Hertweck-Luthar-Passi method (with L. Margolis). GAP package. Link.
  • On torsion subgroups and their normalizers in integral group rings. Dissertation, University of Stuttgart, Germany, 2012. Link.
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Conference

We organized a conference "Groups, Rings and the Yang-Baxter equation" in Spa, Belgium, June 18-24, 2017.
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Teaching

Second semester 2017/2018

  • HOC en WPO Galoistheorie

    • Studenten: 3BA wiskunde
    • Theorie: Dinsdag, 13:00 - 15:00, K.2.Auditorium.3
    • Oefeningen: Maandag, 16:00 - 17:00, F.4.104

Second semester 2016/2017

  • HOC Galoistheorie

    • Studenten: 3BA wiskunde
    • Theorie: Dinsdag, 13:00 - 15:00, F.4.104
    • Oefeningen (Doryan Temmerman): Maandag, 14:00 - 15:00, F.4.103

Second semester 2015/2016

  • HOC Galoistheorie

    • Studenten: 3BA wiskunde
    • Theorie:
      Dinsdag, 13:00 - 15:00, K.2.Auditorium.3, weken 22-23, 25, 27, 31, 33-36
      Woensdag, 08:00 - 10:00, F.5.207, weken 24, 26, 28, 32
    • Oefeningen (Doryan Temmerman): Maandag, 16:00 - 17:00, G.1.022
    • Syllabus op de website van Eric Jespers. Meest recente versie op PointCarré.
    • Een bewijs voor de transcendentie van π.
    • Enkele annotaties van Keith Conrad over Galois groepen: 1 2. Maar er is nog veel meer...
  • WPO Wiskunde: Calculus en Lineaire algebra (deel Lineaire algebra)

    • Titularis: Jan De Beule
    • Studenten: Schakelprogr. M in de Computerwetenschappen
    • Oefeningen:
      Woensdag, 10:00 - 12:00, D.3.14, weken 24-25, 27, 32, 34, 36,
      Donderdag, 15:00 - 17:00, D.2.16, weken 25-26, 28, 32-33

First semester 2014/2015

  • HOC en WPO Galoistheorie

    • Studenten: 3BA wiskunde
    • Theorie: Donderdag, 14:00 - 16:00, G.6.324 (week 2), D.1.08 (week 3-9), D.3.16 (week 11-14)
    • Oefeningen: Dinsdag, 13:00 - 14:00, F.5.203
    • Syllabus op de website van Eric Jespers

First semester 2013/2014

  • HOC Galoistheorie

    • Studenten: 3BA wiskunde
    • Theorie: Donderdag, 14:00 - 16:00, G.6.324
    • Oefeningen (Inneke Van Gelder): Dinsdag, 13:00 - 14:00, G.6.324
    • Syllabus op de website van Eric Jespers

Second semester 2012/2013

  • HOC Inleiding Groepentheorie

    • Studenten: 1BA Wiskunde
    • Theorie: Woensdag, 08:00 - 10:00, F.4.103
    • Oefeningen (Ann Kiefer): Maandag, 09:00 - 11:00, D.2.16
    • Syllabus op de website van Eric Jespers
    • Een alternatief beweijs voor de "Fundamentele Stelling van Eindige Abelse Groepen" (via John M. Sullivan)
  • HOC Representationtheory of finite-dimensional algebras

    • Students: 1st and 2nd year master mathematics
    • Theory: Thursday, 14:00 - 16:00, G.6.324

First semester 2012/2013

  • HOC Galoistheory

    • Students: 3rd year bachelor mathematics
    • Theory: Thursday, 13:30 - 15:30, G.6.324
    • Exercises (Inneke Van Gelder): Thursday, 15:30 - 17:30, G.6.324
    • Lecture notes (in dutch) can be found on the website of Eric Jespers
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