Publications
Preprints
On integral decomposition of unipotent elements in integral group rings
joint with G. Janssens, submitted, 44 pages, 2023.
arXiv: 2307.14820
Units in Blocks of Defect 1 and the Zassenhaus Conjecture
joint with F. Eisele, submitted, 29 pages, 2022.
arXiv: 2212.06634
Peer-reviewed articles in journals
On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center
joint with D. García-Lucas
Forum Mathematicum, 19 pages, 2023.
Journal | arXiv: 2306.06957
Abelian invariants and a reduction theorem for the modular isomorphism problem
joint with T. Sakurai and M. Stanojkovski
Journal of Algebra, 636, 533-559, 2023.
Journal | arXiv: 2110.10025
Twisted group ring isomorphism problem and infinite cohomology groups
joint with O. Schnabel
Journal of Pure and Applied Algebra, 227 (4), Paper No. 107258, 31 pages, 2023.
Journal | arXiv: 2011.10129
The Modular Isomorphism Problem for small groups – revisiting Eick’s algorithm
joint with T. Moede
Journal of Computational Algebra, 1-2, 7 pages, 2022
Journal | arXiv: 2010.07030
The Modular Isomorphism Problem: a survey
Jahresbericht der Deutschen Mathematikervereinigung, 124 (3), 157-196, 2022
Journal | arXiv: 2202.11412
Non-isomorphic 2-groups with isomorphic modular group algebras
joint with D. García-Lucas and Á. del Río
Journal für reine und angewandte Mathematik (Crelles Journal), 783, 269-274, 2022
Journal | arXiv: 2106.07231
On the Modular Isomorphism Problem for groups of class 3
joint with M. Stanojkovski
Journal of Group Theory 25 (1), 163-206, 2022
Journal | arXiv: 2009.13970
Abelianization of the unit group of an integral group ring
joint with A. Bächle and S. Maheshwary
Pacific Journal of Mathematics 321 (2), 309-334, 2021
Journal | arXiv: 2004.03173
GAP-file referred to in the article
Orders of units in integral group rings and blocks of defect 1
joint with M. Caicedo
Journal of the London Mathematical Society 103 (4), 1515-1546, 2021
Journal | arXiv: 1906.03570
From examples to methods: Two cases from the study of units in integral group rings
joint with A. Bächle
Indian Journal of Pure and Applied Mathenatics 52, 669-686, 2021
Special volume on the topics of the academic activity at Group Algebras, Representations and Computation 2019 held at the ICTS Bangalore
Journal | arXiv: 2006.09031
The twisted group ring isomorphism problem over fields
joint with O. Schnabel
Israel Journal of Mathematics 238 (1), 209-242, 2020
Journal | arXiv: 1902.04281
Finite Subgroups of Group Rings: A survey
joint with Á. del Río
Advances in Group Theore and Applications 8, 1-37, 2019
Journal | arXiv: 1809.00718
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
Zassenhaus Conjecture on torsion units holds for $\operatorname{PSL}(2,p)$ 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
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
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
A Counterexample to the First Zassenhaus Conjecture
joint with F. Eisele
Advances in Mathematics 339, 599-641, 2018
Journal | arXiv: 1710.08780
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
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
Cliff-Weiss Inequalities and the Zassenhaus Conjecture
joint with Á. del Río
Journal of Algebra 507, 292-319, 2018
Journal | arXiv: 1706.02483
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
Twisted group ring isomorphism problem
joint with O. Schnabel
The Quarterly Journal of Mathematics 69 (4), 1195-1219, 2018
Journal | arXiv: 1611.00499
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
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
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
GAP-file referred to in the article
Subgroup isomorphism problem for units of integral group rings
Journal of Group Theory 20 (2), 289-307, 2017
Journal | arXiv: 1511.04550
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
A Sylow theorem for the integral group ring of $\operatorname{PSL}(2,q)$
Journal of Algebra 445 (2), 295-306, 2016
Journal | arXiv: 1408.6075
Torsion subgroups in the units of the integral group ring of $\operatorname{PSL}(2,p^3)$
joint with A. Bächle
Archiv der Mathematik (Basel) 105 (1), 1-11, 2015
Journal | arXiv: 1412.7700
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
Peer-reviewed articles in conference proceedings
p-subgroups of units in $\mathbb{Z}G$
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
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
Community service
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
Software
ModIsomExt (with T. Moede). GAP Package. Link
HeLP - The Hertweck-Luthar-Passi method (with A. Bächle). GAP package. Available from GAP 4.8.3 Link