Dear GAP Forum,

Further to Professor Neubueser's email of last Tuesday, there are
functions for systems of common representatives in the utils part
of the xmod share package, as the listing below illustrates.

Best wishes, Chris Wensley

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gap> RequirePackage( "xmod" );;
gap> s4 := SymmetricGroup( 4 );;
gap> c4 := Subgroup( s4, [(1,2,3,4)] );;
gap> CommonTransversal( s4, c4 );
[ (), (3,4), (2,3), (1,2), (1,4), (2,4) ]
gap> IsCommonTransversal( s4, c4, [ (),(1,2),(2,3),(3,4),(1,3),(1,4) ] );
true
gap> L1 := [ [1,2,3], [3,4], [3,4], [1,2,4] ];;
gap> L2 := [ [3,4], [1,2], [2,3], [2,3,4] ];
[ [ 3, 4 ], [ 1, 2 ], [ 2, 3 ], [ 2, 3, 4 ] ]
gap> CommonRepresentatives( L1, L2 );
[ [ 3, 3, 3, 1 ], [ 1, 3, 4, 2 ] ]
gap> # i.e. 3 in L1[1] & L2[1];  3 in L1[2] & L2[3];
gap> #      3 in L1[3] & L2[4];  1 in L1[4] & L2[2].