Nicholson, J;
(2020)
A cancellation theorem for modules over integral group rings.
Mathematical Proceedings of the Cambridge Philosophical Society
pp. 1-11.
10.1017/s0305004120000237.
(In press).
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Abstract
A long standing problem, which has its roots in low-dimensional homotopy theory, is to classify all finite groups G for which the integral group ring ℤG has stably free cancellation (SFC). We extend results of R. G. Swan by giving a condition for SFC and use this to show that ℤG has SFC provided at most one copy of the quaternions ℍ occurs in the Wedderburn decomposition of the real group ring ℝG. This generalises the Eichler condition in the case of integral group rings.
| Type: | Article |
|---|---|
| Title: | A cancellation theorem for modules over integral group rings |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/s0305004120000237 |
| Publisher version: | https://doi.org/10.1017/s0305004120000237 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10119460 |
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