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Nebe, Gabriele

Finite subgroups of \(\text{GL}_{24}(\mathbb{Q})\). (English) Zbl 0870.20029

Exp. Math. 5, No. 3, 163-195 (1996).
The author provides a full list of maximal finite irreducible subgroups \(G\) of \(\text{GL}(n,\mathbb{Z})\) together with their \(G\)-lattices of minimal determinant. The information given is very precise, and contains such parameters as the determinant of the lattice and the number of vectors of minimal length. A \(G\)-invariant quadratic form is given for every primitive group \(G\).
Reviewer: A.E.Zalesskij (Norwich)

Cited in 8 Documents

MSC:

20G20 Linear algebraic groups over the reals, the complexes, the quaternions
11E57 Classical groups
11H56 Automorphism groups of lattices
20C10 Integral representations of finite groups
20E28 Maximal subgroups
20H15 Other geometric groups, including crystallographic groups
20E07 Subgroup theorems; subgroup growth

Keywords:

finite rational linear groups; integral lattices; lattices of minimal determinant; maximal finite irreducible subgroups; vectors of minimal length; primitive groups

Software:

GAP
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Full Text: DOI EuDML EMIS

References:

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