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On maximal finite irreducible subgroups of $ {\rm GL}(n,\,{\bf Z})$. V. The eight-dimensional case and a complete description of dimensions less than ten


Authors: Wilhelm Plesken and Michael Pohst
Journal: Math. Comp. 34 (1980), 277-301
MSC: Primary 20C10
MathSciNet review: 551305
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Abstract: All maximal finite (absolutely) irreducible subgroups of $ GL(8,{\mathbf{Z}})$ are determined up to Z-equivalence. Moreover, we present a full set of representatives of the Z-classes of the maximal finite irreducible subgroups of $ GL(n,{\mathbf{Z}})$ for $ n \leqslant 9$ by listing generators of the groups, the corresponding quadratic forms fixed by these groups, and the shortest vectors of these forms.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1980-0551305-0
Keywords: Integral matrix groups
Article copyright: © Copyright 1980 American Mathematical Society