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STABLY FREE MODULES OVER $\mathbf{Z}[(C_{p}\rtimes C_{q})\times C_{\infty }^{n}]$ ARE FREE

Part of: Rings and algebras arising under various constructions Grothendieck groups and $K_0$

Published online by Cambridge University Press:  22 February 2017

J. D. P. Evans
J. D. P. Evans*
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, U.K. email zcahf50@ucl.ac.uk
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Abstract

Let $p,q$ be primes such that $q|p-1$ and set $\unicode[STIX]{x1D6F7}=C_{p}\rtimes C_{q}$, $G=\unicode[STIX]{x1D6F7}\times C_{\infty }^{n}$ and $\unicode[STIX]{x1D6EC}=\mathbf{Z}[G]$, the integral group ring of $G$. By means of a fibre square decomposition, we show that stably free modules over $\unicode[STIX]{x1D6EC}$ are necessarily free.

MSC classification

Primary: 19A13: Stability for projective modules
Secondary: 16S34: Group rings , Laurent polynomial rings
Type
Research Article
Information
Mathematika , Volume 63 , Issue 2 , 2017 , pp. 451 - 461
Copyright
Copyright © University College London 2017 

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