# 7.10 AsGroup

AsGroup( D )

Let D be a domain. AsGroup returns a group G such that the set of elements of D is the same as the set of elements of G if this is possible.

If D is a list of group elements these elements must form a group. Otherwise an error is signaled.

Note that this function returns a parent group or a subgroup of a parent group depending on D. In order to convert a subgroup into a parent group you must use Group (see Group).

gap> s4 := AgGroup( Group( (1,2,3,4), (2,3) ) );
Group( g1, g2, g3, g4 )
gap> Elements( last );
[ IdAgWord, g4, g3, g3*g4, g2, g2*g4, g2*g3, g2*g3*g4, g2^2, g2^2*g4,
g2^2*g3, g2^2*g3*g4, g1, g1*g4, g1*g3, g1*g3*g4, g1*g2, g1*g2*g4,
g1*g2*g3, g1*g2*g3*g4, g1*g2^2, g1*g2^2*g4, g1*g2^2*g3,
g1*g2^2*g3*g4 ]
gap> AsGroup( last );
Group( g1, g2, g3, g4 )

The default function GroupOps.AsGroup for a group D returns a copy of D. If D is a subgroup then a subgroup is returned. The default function GroupElementsOps.AsGroup expects a list D of group elements forming a group and uses successively Closure in order to compute a reduced generating set.

GAP 3.4.4
April 1997