On maximal finite irreducible subgroups of ${\rm GL}(n, {\bf Z})$. I. The five and seven dimensional cases
On maximal finite irreducible subgroups of ${\rm GL}(n, {\bf Z})$. I. The five and seven dimensional cases
General methods for the determination of maximal finite absolutely irreducible subgroups of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L left-parenthesis n comma bold upper Z right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:mi>L</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">Z</mml:mi> </mml:mrow> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">GL(n,{\mathbf {Z}})</mml:annotation> </mml:semantics> …