Take the tour ×  For several years people have tried to
characterize finite groups of maximal order in
$\mathrm{GL}(n,\mathbb{Q})$ (or $\mathrm{GL}(n,\mathbb{Z})$) and
their orders. It appear in many articles a reference to an
"preprint" article from Walter Feit in 1995 that gave full
characterization. And I read a quote that Feit's paper also
relies on a unpublished paper from Weisfeiler.  Does anyone know
of a (pucblished) paper on this?  share|improve this question
add comment  2 Answers  up vote 9 down vote accepted  Feit
published his paper in the proceedings of the first Jamaican
conference, MR1484185. He defines M(n,K) to be the group of
monomial matrices whose entries are roots of unity. M(n,Q) is
the group of signed permutation matrices.  Theorem A: A finite
subgroup of GL(n,Q) of maximum order is conjugate to M(n,Q) and
so has order n!2^n except in the following cases...
[n=2,4,6,7,8,9,10]. In all cases the finite subgroup of maximum
order in GL(n,Q) is unique up to conjugacy.  He notes that the
max