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