DoubleCoset( U, u, V )
DoubleCoset returns the double coset with representative u and left
group U and right group V. U and V must have a common parent and
u must lie in this parent, otherwise an error is signaled. Double
cosets are domains, so all domain function are applicable to double
cosets (see chapter Domains and Set Functions for Double Cosets).
gap> G := Group( (1,2), (1,2,3,4) );;
gap> U := Subgroup( G, [ (1,2), (3,4) ] );;
gap> D := DoubleCoset( U, (1,2,3), U );
DoubleCoset( Subgroup( Group( (1,2), (1,2,3,4) ), [ (1,2), (3,4) ] ),
(1,2,3), Subgroup( Group( (1,2), (1,2,3,4) ), [ (1,2), (3,4) ] ) )
gap> Size( D );
16
DoubleCosets (see DoubleCosets) computes the set of all double cosets
of two subgroups in a group.
DoubleCoset calls U.operations.DoubleCoset(U,u,V) and returns
that value.
The default function called this way is GroupOps.DoubleCoset, which
creates a double coset record (see Double Coset Records) with the
Set Functions for Double Cosets). Look up DoubleCosets in the index to see for which groups
this function is overlaid.
GAP 3.4.4