[GAP Forum] bug with semidirect product?

[Stefan Kohl]

Dear Forum,

Vdovin Evgeni wrote:

> When I try to construct semidirect product GL_2(9)*GF(9)^2, it returns a 
> group with GF(3)^2 as a normal subgroup (see the listing below).
> 
> gap> V:=GF(9)^2;
> ( GF(3^2)^2 )
> gap> G:=GeneralLinearGroup(2,9);
> GL(2,9)
> gap> p:=SemidirectProduct(G,V);
> <matrix group of size 466560 with 3 generators>
> gap> L:=Image(Embedding(p,1));
> Group(
> [ [ [ Z(3^2), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3) ], [ 0*Z(3), 
> 0*Z(3),
>           Z(3)^0 ] ],
>  [ [ Z(3), Z(3)^0, 0*Z(3) ], [ Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3),
>           Z(3)^0 ] ] ])
> gap> U:=Image(Embedding(p,2));
> Group(
> [ [ [ Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3) ], [ Z(3)^0, 
> 0*Z(3),
>           Z(3)^0 ] ],
>  [ [ Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3) ],
>      [ 0*Z(3), Z(3)^0, Z(3)^0 ] ] ])
> gap> Order(U);
> 9
> 
> Can anybody explain, what is wrong here?

Thanks for the report.

In fact this is a known bug, which will be fixed in the next release:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Date
2007/01/17
! Changed by
AH
! Reported by
anvita21
! Type of Change
Fix: wrong result
! Description
When forming the semidirect product of a matrix group with a vector space
over a non-prime field
the embedding of the vector space gives a wrong result.
! Changed Files
lib/gprd.gi
! End
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

If you need a workaround for this bug already now, then please write to
support at gap-system.org .

Best wishes,

     Stefan Kohl