IsNaturalGL( matgrp ) P
This property tests, whether a matrix group is the General Linear group in the right dimension over the (smallest) ring which contains all entries of its elements.
IsGeneralLinearGroup( grp ) P
IsGL( grp ) P
The General Linear group is the group of all invertible matrices over a ring. This property tests, whether a group is isomorphic to a General Linear group.
IsNaturalSL( matgrp ) P
This property tests, whether a matrix group is the Special Linear group in the right dimension over the (smallest) ring which contains all entries of its elements.
IsSpecialLinearGroup( grp ) P
IsSL( grp ) P
The Special Linear group is the group of all invertible matrices over a ring. This property tests, whether a group is isomorphic to a Special Linear group.
gap> IsNaturalGL(m); false
IsSubgroupSL( matgrp ) P
This property tests, whether a matrix group is a subgroup of the Special Linear group in the right dimension over the (smallest) ring which contains all entries of its elements.
(See also section Classical Groups.)
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GAP 4 manual