Dear forum,

I have another problem using 'Projection()' from the 'SubdirectProduct()':
an error occurs when I try to use 'PreImagesRepresentative():

# again the example usage of 'SubdirectProduct()' from the GAP manual
s3 := Group( (1,2,3), (1,2) );;
c3 := Subgroup( s3, [ (1,2,3) ] );;
x1 := Operation( s3, Cosets( s3, c3 ), OnRight );;
h1 := OperationHomomorphism( s3, x1 );;
d8 := Group( (1,2,3,4), (2,4) );;
c4 := Subgroup( d8, [ (1,2,3,4) ] );;
x2 := Operation( d8, Cosets( d8, c4 ), OnRight );;
h2 := OperationHomomorphism( d8, x2 );;
s := SubdirectProduct( s3, d8, h1, h2 );

# compute the projection and copy entries from the direct product
# to fix the bug earlier mentioned
p1_s := Projection(s, s3, 1);
d12 := DirectProduct(s3, d8);
s.news := d12.news;
s.perms := d12.perms;
s.olds := d12.olds;

# try to use 'PreImagesReresentative()' on an arbitrary element of
# the image of the projection
x := Random(Image(p1_s, p1_s.source));
PreImagesRepresentative( p1_s, x );

GAP responds:

Error, Record: element 'perms' must have an assigned value at
elm := img ^ prj.range.perms[prj.component] ... in
map.operations.PreImagesRepresentative( map, img ) called from
PreImagesRepresentative( p1_s, x ) called from
main loop
brk>

Ottokar Kulendik