Vrije Universiteit Brussel


Dr. Leo Margolis

Personal information

My coordinates

  • Address: Vrije Universiteit Brussel
    DWIS
    Pleinlaan 2
    B-1050 Brussels
    Belgium
  • Office: G.6.323
  • Phone: +32 2 629 34 67
  • E-mail:
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Research

Research interests

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

Submitted manuscripts / Preprints (in reverse chronological order)

  1. Orders of units in integral group rings and blocks of defect 1
    joint with M. Caicedo, submitted, 26 pages, 2019.
    arXiv:1906.03570 [math.GR]

Published and accepted articles (in reverse chronological order)

  1. The twisted group ring isomorphism problem over fields
    joint with O. Schnabel, to appear in Israel Journal of Mathematics, 24 pages, 2019.
    arXiv:1902.04281 [math.RA]

  2. Finite Subgroups of Group Rings: A survey
    joint with Á. del Río, to appear in Advances in Group Theore and Applications, 23 pages, 2018.
    arXiv:1809.00718 [math.GR]

  3. An application of blocks to torsion units in group rings
    joint with A. Bächle.
    Proceedings of the American Mathematical Society, 147, 4221-4231, 2019.
    Journal | arXiv:1808.07820 [math.RA]

  4. Zassenhaus Conjecture on torsion units holds for PSL(2,p) with p a Fermat or Mersenne prime
    joint with Á. del Río and M. Serrano.
    Journal of Algebra, 531, 320-335, 2019.
    Journal | arXiv:1608.05797 [math.RA].

  5. On the Prime Graph Question for Integral Group Rings of Conway simple groups
    Journal of Symbolic Computation, 95 , 162-176, 2019.
    Journal | arXiv:1711.11322 [math.RA].

  6. The Herzog-Schönheim Conjecture for small groups and harmonic subgroups
    joint with O. Schnabel,
    Beiträge zur Algebra und Geometrie, 60 (3), 399-418, 2019.
    Journal | arXiv:1803.03569 [math.GR].

  7. A Counterexample to the First Zassenhaus Conjecture
    joint with F. Eisele.
    Advances in Mathematics, 339, 599-641, 2018.
    Journal | arXiv:1710.08780 [math.RA].

  8. An algorithm to construct candidates to counterexamples to the Zassenhaus Conjecture
    joint with Á. del Río.
    Journal of Algebra, 514, 536-558, 2018.
    Journal | arXiv:1710.05629 [math.RA].

  9. Partial Augmentations Power property: A Zassenhaus Conjecture related problem
    joint with Á. del Río.
    Journal of Pure and Applied Algebra, 223 (9), 4089-4101, 2019.
    Journal | arXiv:1706.04787 [math.RA].

  10. Cliff-Weiss Inequalities and the Zassenhaus Conjecture
    joint with Á. del Río.
    Journal of Algebra 507, 292-319, 2018.
    Journal | arXiv:1706.02483 [math.GR].

  11. HeLP -- A GAP package for torsion units in integral group rings
    joint with A. Bächle.
    Journal of Software for Algebra and Geometry 8, 1-9, 2018.
    Journal | arXiv:1507.08174 [math.RT].

  12. Twisted group ring isomorphism problem
    joint with O. Schnabel.
    The Quarterly Journal of Mathematics 69 (4), 1195-1219, 2018.
    Journal | arXiv:1611.00499 [math.RA].

  13. On the Prime Graph Question for Integral Group Rings of 4-primary groups II
    joint with A. Bächle.
    Algebras and Representation Theory, 22 (2), 437-457, 2019
    Journal | arXiv:1606.01506 [math.RT].

  14. Algorithmic aspects of units in group rings
    joint with A. Bächle & W. Kimmerle.
    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].

  15. The status of the Zassenhaus conjecture for small groups
    joint with A. Bächle, A. Herman, A. Konovalov & G. Singh.
    Experimental Mathematics 27 (4), 431-436, 2018.
    Journal | arXiv:1609.00042 [math.RA].

  16. On the Prime Graph Question for Integral Group Rings of 4-primary groups I
    joint with A. Bächle.
    International Journal of Algebra and Computation 27(6), 731-767, 2017.
    Journal | arXiv:1601.05689 [math.RT] | GAP-file referred to in the article.

  17. p-subgroups of units in ZG
    joint with W. Kimmerle.
    Groups, rings, group rings, and Hopf algebras, Contemporary Mathematics 688 Amer. Math. Soc., Providence, p. 169-179, 2017.
    Book | arXiv:1605.09599 [math.RA].

  18. Subgroup isomorphism problem for units of integral group rings
    Journal of Group Theory 20(2), 289-307, 2017.
    Journal | arXiv:1511.04550 [math.RA].

  19. Rational conjugacy of torsion units in integral group rings of non-solvable groups
    joint with A. Bächle.
    Proceedings of the Edinburgh Mathematical Society 60(4), 813-830, 2017.
    Journal | arXiv:1305.7419 [math.RT].

  20. A Sylow theorem for the integral group ring of PSL(2,q).
    Journal of Algebra 445(2), 295-306, 2016.
    Journal | arXiv:1408.6075 [math.RA].

  21. Torsion subgroups in the units of the integral group ring of PSL(2,p3)
    joint with A. Bächle.
    Archiv der Mathematik (Basel) 105(1):1-11, 2015.
    Journal | arXiv:1412.7700 [math.GR].

  22. Zassenhaus conjecture for cyclic-by-abelian groups
    joint with Á. del Río & M. Caicedo.
    Journal of the London Mathematical Society. Second Series 88(1):65-78, 2013.
    Journal | arXiv:1202.3877 [math.RT].

Co-authors: Andreas Bächle, Mauricio Caicedo, Florian Eisele, Allen Herman, Wolfgang Kimmerle, Alexander Konovalov, Ángel del Río, Mariano Serrano, Ofir Schnabel, Gurmail Singh.

Community service

  1. A theorem of Hertweck on p-adic conjugacy of p-torsion units in group rings.
    not intended for peer-reviewed publication, since only reproducing an important result of M. Hertweck which was not published elsewhere, 11 pages, 2017.
    arXiv:1706.02117 [math.RA].

Software

  • HeLP - The Hertweck-Luthar-Passi method (with A. Bächle). GAP package. Available from GAP 4.8.3 Link.
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Conference

We organized a conference

Groups, Rings and Associated Strucutres,

aka GRAS 2019 in Spa, Belgium, June 9-15, 2019.
It was a sequel to Groups, Rings and the Yang-Baxter equation also held in Spa, June 18-24, 2017.
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Teaching

Second semester 2018/2019

  • HOC en WPO Galoistheorie

    • Studenten: 3BA wiskunde
    • Theorie: Woensdag, 10:00 - 12:00
    • Oefeningen: Maandag, 16:00 - 18:00

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
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Talks

Seminar talks

    2018 - 2019

  • Blocks of defect 1 and units in integral group rings. Algebra Seminar, Bar Ilan University, Ramat Gan, Israel, September 26th 2019.
  • Blocks of defect 1 and units in integral group rings. AG Algebra, Geometrie und Computeralgebra, Technische Universität Kaiserslautern, Kaiserslautern, Germany, July 11th 2019.
  • A counterexample to the (first) Zassenhaus conjecture. Actions!, Université de Lyon, Lyon, France, April 30th 2019.
  • Orders of units in group rings. Algebra seminar, Universitä Bielefeld, Bielefeld, Germany, April 17th 2019.
  • A counterexample to the (first) Zassenhaus conjecture. Algebra seminar, Università di Padova, Padova, Italy, February 22nd 2019.
  • A counterexample to the (first) Zassenhaus conjecture. Oberseminar Algebra, Technische Universität Braunschweig, Braunschweig, Germany, January 22nd 2019.
  • A counterexample to the first Zassenhaus conjecture. Oberseminar Algebra, Universität Stuttgart, Stuttgart, Germany, December 18th 2018.
  • A counterexample to the first Zassenhaus conjecture for units in integral group rings. Fachbereichskolloquium Mathematik, Universität Stuttgart, Stuttgart, Germany, December 17th 2018.
  • The group ring and its units. Math Colloquim, Ort Braude College, Karmiel, Israel, November 6th 2018.
  • Blocks, characters and torsion units in integral group rings. Algebra and Number Theory Seminar, Technion, Haifa, Israel, November 4th 2018.
  • A counterexample to the first Zassenhaus conjecture. Seminar des Lehrstuhls D, RWTH Aachen, Aachen, Germany, July 12th 2018.
  • The Zassenhaus Conjecture. ALGB Seminar, Vrije Universiteit Brussel, Brussels, Belgium, February 14th and 15th 2018.
  • 2016 - 2017

  • A counterexample to the first Zassenhaus conjecture. Algebra Seminar University of Haifa, Haifa, Israel, December 14th 2017.
  • The group ring and its units. Colloquium Technion, Haifa, Israel, December 11th 2017.
  • A counterexample to the first Zassenhaus conjecture. Algebra Seminar Technion, Haifa, Israel, December 7th 2017.
  • Torsion Units in Integral Group Rings and the Zassenhaus Conjecture. Group Theory Seminar, Universidad Autónoma Madrid-ICMAT, Madrid, Spain, October 4th, 2017.
  • Zassenhaus Conjecture for small groups. Algebra Seminar Universidad de Murcia, Murcia, Spain, October 20th 2016.
  • Torsion units in Integral Group Rings. Algebra Seminar Universitat de València, València, Spain, September 16th 2016.
  • Torsion units in Integral Group Rings. Math Colloquium, Florida Atlantic University, Boca Raton, Florida, USA, September 2nd 2016.
  • 2011 - 2015

  • Torsion subgroups in the Unit Group of Integral Group Rings. Oberseminar Algebra/Zahlentheorie, Universität Jena, Jena, Germany, Decemeber 1st 2015.
  • The Zassenhaus Conjecture for Integral Group Rings. Oberseminar Algebra, Universität Osnabrück, Osnabrück, Germany, November 10th 2015.
  • Torsion Units in Integral Group Rings. Oberseminar Gruppen und Geometrie, Universität Bielefeld, Bielefeld, Germany, October 21st 2015.
  • Sylow Theorems for the Unit Group of the Integral Group Ring. Algebra Seminar Universidad de Murcia, Murcia, Spain, January 22nd 2015.
  • Rational Conjugacy of Torsion Units in Group Rings. ALGB Seminar, Vrije Universiteit Brussel, Brussels, Belgium, December 10th 2014.
  • Zassenhaus Conjecture and Prime Graph Question for Group Rings. Oberseminar Algebra, University of Stuttgart, Stuttgart, Germany, June 24th 2014.
  • Rational conjugacy of torsion units in integral group rings of non-solvable groups. Oberseminar Algebra, University of Stuttgart, Stuttgart, Germany, January 29th 2013
  • Small subgroups of units in the Integral Group Ring. Oberseminar Algebra, University of Stuttgart, Stuttgart, Germany, May 18th 2012
  • Free subgroups in the Integral Group Ring and dihedral p-critical elements. Oberseminar Algebra, University of Stuttgart, Stuttgart, Germany, July 7th 2011

Conference talks

    2017 - 2019

  • Blocks of defect 1 and units in integral group rings. Advances in Group Theory and Applications 2019, Lecce, Italy, June 25th - 28th 2019.
  • Units in Group Rings and Blocks of Defect 1. Groups, Rings and Associated Structures, Spa, Belgium, June 9th - 15th 2019.
  • Blocks, characters and units in group rings. Representations of Finite Groups, Oberwolfach, Germany, March 24th - 30th 2019.
  • Blocks, characters and torsion units in integral group rings. Groups in Madrid 2018, Madrid, Spain, November 22nd - 23rd 2018.
  • A counterexample to the first Zassenhaus Conjecture. Groups in Florence 2018, Florence, Italy, September 5th - 7th 2018.
  • The Herzog-Schönheim Conjecture or: is commutativity overrated?. Groups & Algebras in Bicocca for Young algebraists, Milano, Italy, May 21st- 25th 2018.
  • A counterexample to the first Zassenhaus Conjecture. 2018 Zassenhaus Groups and Friends Conference, Tampa, Florida, USA, April 6th - 8th 2018.
  • La conjetura de Zassenhaus para grupos pequeños. 4º congreso de jóvenes invesigadores, València, Spain, September 4th - 8th 2017.
  • On the Zassenhaus Conjecture for small groups. Groups St Andrews 2017, Birmingham, UK, August 5th - 13th 2017.
  • On a result of Cliff and Weiss about a strategy to attack the Zassenhaus Conjecture. Groups, Rings and the Yang-Baxter equation, Spa, Belgium, June 18th - 24th 2017, Officially not celebrating Eric Jespers' 62nd birthday.
  • Zassenhaus Conjecture for small groups. Young Researchers Algebra Conference 2017, Naples, Italy, May 23rd - 24th 2017.
  • 2015 - 2016

  • Zassenhaus Conjecture for simple groups. Advances in Group Theory and Applications 2016 - The School, Vietri sul Mare, Italy, June 6th - 9th 2016.
  • Subgroup Isomorphism Problem and Sylow theorems in integral group rings. Ischia Group Theory 2016, Ischia, Italy, March 29th - April 2nd 2016.
  • Zassenhaus Conjecture and Prime Graph Question for Integral Group Rings. Special Session on Groups, Rings, Group Rings, and Hopf Algebras (celebrating the 75th birthday of Donald S. Passman), Chicago, Illinois, USA, October 2nd - October 4th 2015.
  • Torsion Units in Integral Group Rings. Jahrestagung DFG Schwerpunkt 1489, Osnabrück, Germany, September 28th - October 2nd 2015.
  • Prime graph question for torsion units in group rings of 4-primary groups. Groups and their Actions, Bedlewo, Poland, June 22nd - 25th 2015.
  • Torsionsuntergruppen in ganzzahligen Gruppenringen. Grüppchen 2015, Gießen, Germany, March 6th - 7th 2015 .
  • 2011 - 2015

  • Representation Theory Applied to Torsion Units in Group Rings. Darstellungstheorietage 2014, Kaiserslautern, Germany, November 7th - 8th 2014.
  • Torsion Units in the Integral Group Ring of PSL(2,p^f). DMV-PTM Joint Meeting 2014, Poznan, Poland, September 16th - 20st 2014.
  • Prime Graph Question for 4-primary groups II. Groups, Rings and Group Rings, St. Catherines, Ontario, Canada, July 28th - August 1st 2014.
  • Zassenhaus Conjecture for cyclic-by-abelian groups. Groups St Andrews 2013, St Andrews, Scotland, August 3rd - 11th 2013,.
  • Rational conjugacy of torsion units in integral group rings of non-solvable groups. Recent Trends in Rings and Algebras, Murcia, Spain, June 3rd - 7th 2013.
  • On the first Zassenhaus Conjecture. Darstellungstheorietage 2012, Magdeburg, Germany, November 23rd - 24th 2012.
  • Zassenhaus Conjecture for cyclic-by-abelian groups. Group Rings and related topics, Stuttgart, Germany, June 25th-29th 2012.
  • Freie Untergruppen in U(ZG) und dieder-kritische Elemente. Studierendenkonferenz der DMV 2011, Cologne, Germany, September 20th - 21st 2011.
  • Dihedral p-critical elements in finite simple groups. Groups, Rings and Group Rings, Edmonton, Alberta, Canada, July 11th - 15th 2011.

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