# [GAP Forum] unpredictable SemidirectProduct

Monson, Barry R bmonson at unb.ca
Mon May 31 17:02:27 BST 2010

```Dear Gap users,
I am puzzled by the behaviour of SemidirectProduct.
Two similar calculations, only one successful, follow.
Can someone explain what, if anything, I am doing wrong?
The problem may have something to
do with `immutable compressed matrices'.

Thanks,
Barry.
#######################################
gap> r0:=(1,2);;r1:=(2,3);;G:=Group(r0,r1);
Group([ (1,2), (2,3) ])
gap> u:=Z(5)^0;
Z(5)^0
gap> m0:=u*[[0,1],[1,0]];; m1:=u*[[1,0],[-1,-1]];;
gap> Mat:=Group(m0,m1);;IsSubgroup(GL(2,5),Mat);
true
gap> N:=GF(5)^2;;
gap> alpha:=GroupHomomorphismByImages(G,Mat,[r0,r1],[m0,m1]);;
gap> sem:=SemidirectProduct(G,alpha,N);
<matrix group of size 150 with 3 generators>
gap> # So far, so good; 150 = 6*25.
gap> # Now tweak the inputs a little.
gap> m0:=u*[[1,0,0],[0,1,0],[0,0,1]];;m1:=m0;;
gap> Mat:=Group(m0,m1);IsSubgroup(GL(3,5),Mat);
Group([ [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], [
0*Z(5), 0*Z(5), Z(5)^0 ] ],
[ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], [ 0*Z(5),
0*Z(5), Z(5)^0 ] ] ])
true
gap> # Now we have a trivial action on a 3-dimensional space over GF(5).
gap> N:=GF(5)^3;;
gap> alpha:=GroupHomomorphismByImages(G,Mat,[r0,r1],[m0,m1]);
[ (1,2), (2,3) ] -> [ [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0,
0*Z(5) ], [ 0*Z(5), 0*Z(5), Z(5)^0 ] ]
, [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], [
0*Z(5), 0*Z(5), Z(5)^0 ] ] ]
gap> sem:=SemidirectProduct( G, alpha, N );
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 2nd choice method found for `SemidirectProduct' on 3
arguments called from
<function>( <arguments> ) called from read-eval-loop