Dear Forum!
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?
--
Best Regards
Vdovin Evgenii
Institute of Mathematics
pr-t Acad. Koptyug, 4
630090, Novosibirsk, Russia
Office +7 383 3333495
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