Publications
Preprints
The Modular Isomorphism Problem over all fields
joint with T. Sakurai, submitted, 16 pages, 2025.
arXiv: 2505.05902
Units in group rings and blocks of Klein four or dihedral defect
joint with F. Eisele, submitted, 17 pages, 2024.
arXiv: 2412.09525
Peer-reviewed articles in journals
On integral decomposition of unipotent elements in integral group rings
joint with G. Janssens, Mathematical Proceedings of the Cambridge Philosophical Society (to appear), 46 pages, 2025.
arXiv: 2307.14820
Identification of non-isomorphic 2-groups with dihedral central quotient and isomorphic modular group algebras
joint with T. Sukarai, Revista Matemática Iberoamericana, 26 pages, 2025.
Journal | arXiv: 2405.08075
Units in Blocks of Defect 1 and the Zassenhaus Conjecture
joint with F. Eisele, Revista Matemática Complutense, 38 pages, 2024.
Journal | arXiv: 2212.06634
On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center
joint with D. García-Lucas
Forum Mathematicum, 36 (5), 1321-1340, 2024.
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
ModIsom (from version 3.0.0; with B. Eick, D. García-Lucas, A. Konovalov, T. Moede) GAP Package. Link
ModIsomExt (with T. Moede). GAP Package. Link. Almost all funcionality of this package has now been integrated into ModIsom
HeLP - The Hertweck-Luthar-Passi method (with A. Bächle). GAP package. Available from GAP 4.8.3 Link