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In addition to the functionality explained in
Chapter MATRIX GROUPS OVER INFINITE FIELDS and the functions that are available for all
finite (matrix) groups, Magma can also compute normalizers and
centralizers of a finite integral matrix group G in GLn(Z) as
well as decide conjugacy in GLn(Z) and GLn(Q).
These algorithms are based on the sublattice machinery (see Section
G-invariant Sublattices) and the enumeration of G-perfect forms.
They are explained in [OPS98], [Opg01]. The algorithms
perform very well, as long as the space of G-invariant symmetric
forms has small dimension (say less than 15) and the index of the
groups in their Bravais groups is not too large.
The databases of maximal finite irreducible rational, integral,
symplectic and quaternionic matrix groups are explained in
Chapter DATABASES OF GROUPS.
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