GAP Manual: 21.9. ExtendStabChain

ExtendStabChain( G, lst )

ExtendStabChain inserts trivial stabilizers into the known stabilizer chain of the permutation group G such that lst becomes the base of G. The stabilizer chain which belongs to the base lst must reduce to the old stabilizer chain (see ReduceStabChain).

This function is useful if two different (sub-)groups have to have exactly the same base.

    gap> s4 := Group( (1,2), (1,2,3,4) );;
    gap> MakeStabChain( s4, [3,2,1] );  Base( s4 );
    [ 3, 2, 1 ]
    gap> h := Subgroup( Parent(s4), [(1,2,3,4), (2,4)] );
    Subgroup( Group( (1,2), (1,2,3,4) ), [ (1,2,3,4), (2,4) ] )
    gap> Base( h );
    [ 1, 2 ]
    gap> MakeStabChain( h, Base( s4 ) );  Base( h );
    [ 3, 2 ]
    gap> ExtendStabChain( h, Base( s4 ) );  Base( h );
    [ 3, 2, 1 ]