7.91 IsLeftCoset

IsLeftCoset( obj )

IsLeftCoset returns true if the object obj is a left coset, i.e., a record with the component isLeftCoset with value true, and false otherwise. Will signal an error if obj is an unbound variable.

    gap> C := (1,2) * Subgroup( Group( (1,2), (1,2,3) ), [ (1,2,3) ] );;
    gap> IsLeftCoset( C );
    true
    gap> D := Subgroup( Group( (1,2), (1,2,3) ), [ (1,2,3) ] ) * (1,2);;
    gap> IsLeftCoset( D );
    false    # note that <D> is a *right coset* record,
    gap> C = D;
    true     # though as a set, it is of course also a left coset
    gap> IsLeftCoset( 17 );
    false 

IsRightCoset (see IsRightCoset) tests if an object is a right coset.

Previous Up Top Next
Index