
Dr. Leo Margolis
Personal information
My coordinates
 Address: Vrije Universiteit Brussel
DWIS
Pleinlaan 2
B1050 Brussels
Belgium
 Office: G.6.323
 Phone: +32 2 629 34 67
 Email:
leo.margolis@vub.be
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Research
Research interests
 Group Rings
 Group Theory
 Representation Theory and Applications
 Computer Algebra
Submitted manuscripts / Preprints (in reverse chronological order)
 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)
 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]
 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]
 An application of blocks to torsion units in group rings
joint with A. Bächle.
Proceedings of the American Mathematical Society, 147, 42214231, 2019.
Journal 
arXiv:1808.07820 [math.RA]
 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, 320335, 2019.
Journal  arXiv:1608.05797 [math.RA].
 On the Prime Graph Question for Integral Group Rings of Conway simple groups
Journal of Symbolic Computation, 95 , 162176, 2019.
Journal  arXiv:1711.11322 [math.RA].
 The HerzogSchönheim Conjecture for small groups and harmonic subgroups
joint with O. Schnabel,
Beiträge zur Algebra und Geometrie, 60 (3), 399418, 2019.
Journal  arXiv:1803.03569 [math.GR].
 A Counterexample to the First Zassenhaus Conjecture
joint with F. Eisele.
Advances in Mathematics, 339, 599641, 2018.
Journal  arXiv:1710.08780 [math.RA].
 An algorithm to construct candidates to counterexamples to the Zassenhaus Conjecture
joint with Á. del Río.
Journal of Algebra, 514, 536558, 2018.
Journal  arXiv:1710.05629 [math.RA].
 Partial Augmentations Power property: A Zassenhaus Conjecture related problem
joint with Á. del Río.
Journal of Pure and Applied Algebra, 223 (9), 40894101, 2019.
Journal  arXiv:1706.04787 [math.RA].
 CliffWeiss Inequalities and the Zassenhaus Conjecture
joint with Á. del Río.
Journal of Algebra 507, 292319, 2018.
Journal  arXiv:1706.02483 [math.GR].
 HeLP  A GAP package for torsion units in integral group rings
joint with A. Bächle.
Journal of Software for Algebra and Geometry 8, 19, 2018.
Journal  arXiv:1507.08174 [math.RT].
 Twisted group ring isomorphism problem
joint with O. Schnabel.
The Quarterly Journal of Mathematics 69 (4), 11951219, 2018.
Journal  arXiv:1611.00499 [math.RA].
 On the Prime Graph Question for Integral Group Rings of 4primary groups II
joint with A. Bächle.
Algebras and Representation Theory, 22 (2), 437457, 2019
Journal  arXiv:1606.01506 [math.RT].
 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. 122, 2018.
Book  arXiv:1612.06171 [math.RT].
 The status of the Zassenhaus conjecture for small groups
joint with A. Bächle, A. Herman, A. Konovalov & G. Singh.
Experimental Mathematics 27 (4), 431436, 2018.
Journal  arXiv:1609.00042 [math.RA].
 On the Prime Graph Question for Integral Group Rings of 4primary groups I
joint with A. Bächle.
International Journal of Algebra and Computation 27(6), 731767, 2017.
Journal  arXiv:1601.05689 [math.RT]
 GAPfile referred to in the article.
 psubgroups of units in ZG
joint with W. Kimmerle.
Groups, rings, group rings, and Hopf algebras, Contemporary Mathematics 688 Amer. Math. Soc., Providence, p. 169179, 2017.
Book  arXiv:1605.09599 [math.RA].
 Subgroup isomorphism problem for units of integral group rings
Journal of Group Theory 20(2), 289307, 2017.
Journal  arXiv:1511.04550 [math.RA].
 Rational conjugacy of torsion units in integral group rings of nonsolvable groups
joint with A. Bächle.
Proceedings of the Edinburgh Mathematical Society 60(4), 813830, 2017.
Journal  arXiv:1305.7419 [math.RT].
 A Sylow theorem for the integral group ring of PSL(2,q).
Journal of Algebra 445(2), 295306, 2016.
Journal  arXiv:1408.6075 [math.RA].
 Torsion subgroups in the units of the integral group ring of PSL(2,p^{3})
joint with A. Bächle.
Archiv der Mathematik (Basel) 105(1):111, 2015.
Journal  arXiv:1412.7700 [math.GR].
 Zassenhaus conjecture for cyclicbyabelian groups
joint with Á. del Río & M. Caicedo.
Journal of the London Mathematical Society. Second Series 88(1):6578, 2013.
Journal  arXiv:1202.3877 [math.RT].
Coauthors: Andreas Bächle, Mauricio Caicedo, Florian Eisele, Allen Herman, Wolfgang Kimmerle, Alexander Konovalov, Ángel del Río, Mariano Serrano, Ofir Schnabel, Gurmail Singh.
Community service
 A theorem of Hertweck on padic conjugacy of ptorsion units in group rings.
not intended for peerreviewed 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 HertweckLutharPassi method (with A. Bächle). GAP package. Available from GAP 4.8.3 Link.
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Conference
We organized a conference aka GRAS 2019 in Spa, Belgium, June 915, 2019.
It was a sequel to Groups, Rings and the YangBaxter equation also held in Spa, June 1824, 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 MadridICMAT, 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 nonsolvable 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 pcritical 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 HerzogSchönheim 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 YangBaxter 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 4primary 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). DMVPTM Joint Meeting 2014, Poznan, Poland, September 16th  20st 2014.
 Prime Graph Question for 4primary groups II. Groups, Rings and Group Rings, St. Catherines, Ontario, Canada, July 28th  August 1st 2014.
 Zassenhaus Conjecture for cyclicbyabelian groups. Groups St Andrews 2013, St Andrews, Scotland, August 3rd  11th 2013,.
 Rational conjugacy of torsion units in integral group rings of nonsolvable 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 cyclicbyabelian groups. Group Rings and related topics, Stuttgart, Germany, June 25th29th 2012.
 Freie Untergruppen in U(ZG) und diederkritische Elemente. Studierendenkonferenz der DMV 2011, Cologne, Germany, September 20th  21st 2011.
 Dihedral pcritical elements in finite simple groups. Groups, Rings and Group Rings, Edmonton, Alberta, Canada, July 11th  15th 2011.

