Eisele, F. and Margolis, L. (2018) A counterexample to the first Zassenhaus conjecture. Advances in Mathematics, 339, pp. 599-641. (doi: 10.1016/j.aim.2018.10.004)
|
Text
177223.pdf - Accepted Version Available under License Creative Commons Attribution Non-commercial No Derivatives. 525kB |
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.
| Item Type: | Articles |
|---|---|
| Additional Information: | The first author was supported by the EPSRC, grant EP/M02525X/1. The second author was supported by a Marie Curie Individual Fellowship from the European Commissions H2020 project 705112-ZC and the FWO (Research Foundation Flanders). |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Eisele, Dr Florian |
| Authors: | Eisele, F., and Margolis, L. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics |
| Journal Name: | Advances in Mathematics |
| Publisher: | Elsevier |
| ISSN: | 0001-8708 |
| ISSN (Online): | 1090-2082 |
| Published Online: | 04 October 2018 |
| Copyright Holders: | Copyright © 2018 Elsevier Inc. |
| First Published: | First published in Advances in Mathematics 339: 599-641 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
University Staff: Request a correction | Enlighten Editors: Update this record
Deposit and Record Details
Deposit and Record Details