U * u
Coset( U, u )
RightCoset( U, u )
Coset( U )
RightCoset( U )
The first three forms return the right coset of the subgroup U with the representative u. u must lie in the parent group of U, otherwise an error is signalled. In the last two forms the right coset of U with the identity element of the parent of U as representative is returned. In each case the right coset is returned as a domain, so all domain functions are applicable to right cosets (see chapter Domains and Set Functions for Right Cosets).
gap> G := Group( (1,2), (1,2,3,4) );;
gap> U := Subgroup( G, [ (1,2), (3,4) ] );;
gap> U * (1,2,3);
(Subgroup( Group( (1,2), (1,2,3,4) ), [ (1,2), (3,4) ] )*(1,2,3))
RightCosets (see RightCosets) computes the set of all right cosets of
a subgroup in a group. LeftCoset (see LeftCoset) constructs left
cosets.
RightCoset calls U.operations.RightCoset( U, u ) and returns
that value.
The default function called this way is GroupOps.RightCoset, which
creates a right coset record (see Right Cosets Records) with the
Set Functions for Right Cosets). Look up the entries for RightCoset in the index to see for
which groups this function is overlaid.
GAP 3.4.4