A counterexample to the first Zassenhaus conjecture
Eisele, F. 
ORCID: 0000-0001-8267-2094 & Margolis, L. (2018).
A counterexample to the first Zassenhaus conjecture.
Adavances in Mathematics, 339,
pp. 599-641.
doi: 10.1016/j.aim.2018.10.004
Abstract
Hans J. Zassenhaus conjectured that for any unit u of finite order in the integral group ring of a finite group G there exists a unit a in the rational group algebra of G such that a−1· u · a = ±g for some g ∈ G. We disprove this conjecture by first proving general results that help identify counterexamples and then providing an infinite number of examples where these results apply. Our smallest example is a metabelian group of order 27·32·5·72·192 whose integral group ring contains a unit of order 7 · 19 which, in the rational group algebra, is not conjugate to any element of the form ±g.
| Publication Type: | Article |
|---|---|
| Additional Information: | © Elsevier 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Publisher Keywords: | Unit group, Group ring, Zassenhaus conjecture, Integral representations |
| Subjects: | Q Science > QA Mathematics |
| Departments: | School of Science & Technology > Mathematics |
| SWORD Depositor: |
Available under License Creative Commons Attribution Non-commercial No Derivatives.
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