[GAP Forum] bug with semidirect product?

[Rudolf Zlabinger]

Dear Forum,

there is something wrong with that semidirect product in general:

The Reference Manual says for SemidirectProduct(autgrp,N) (the second 
variant), as used in our case:

In the second variant, autgp must be a group of automorphism of N, it is a 
shorthand for SemidirectProduct(autgp,IdentityMapping(autgp),N). Note that 
(unless autgrp has been obtained by the operation AutomorphismGroup) you 
have to test IsGroupOfAutomorphisms(autgrp) to ensure that GAP knows that 
autgrp consists of group automorphisms.

As the conditions dont hold in the following way:

gap> v:=GF(9)^2;
( GF(3^2)^2 )
gap> g:=GL(2,9);
GL(2,9)
gap> IsGroupOfAutomorphisms(g);
false
gap>

the result is not well defined by function description, and may be wrong in 
any way.

best regards, Rudolf Zlabinger







----- Original Message ----- 
From: "Stefan Kohl" <kohl at mathematik.uni-stuttgart.de>
To: "GAP Forum" <forum at gap-system.org>
Sent: Tuesday, June 19, 2007 1:38 PM
Subject: Re: [GAP Forum] bug with semidirect product?


> 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
>
>
>
>
>
>
>
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