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A cancellation theorem for modules over integral group rings

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). Green open access

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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 > 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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