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

• Published in: Mathematika Vol. 63; no. 2; pp. 451 - 461
• Main Author: Evans, J. D. P.
• Format: Journal Article
• Language: English
• Published: London, UK London Mathematical Society 2017
• Subjects: 19A13 (primary); 16S34 (secondary)
• ISSN: 0025-5793; 2041-7942
• DOI: 10.1112/S0025579316000395

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.