GAP Forum: Semi-direct product

> < ^ Date: Mon, 20 Aug 2001 21:46:37 +0200
> < ^ From: Nicola Sottocornola <n_sotto@club-internet.fr >
> ^ Subject: Semi-direct product

--------------EAC4D3A17EBEE52EB2BB05A1
Content-Type: text/plain; charset=us-ascii; x-mac-type="54455854"; x-mac-creator="4D4F5353"
Content-Transfer-Encoding: 7bit

Dear Gap-forum,

I have 2 matrix A and S defined in this way

e:=CyclotomicField( 12 );;
idm:=IdentityMat(4,e);;
i:=E(4);;
co:=(E(6)+(E(6))^(-1))/2;;
si:=(E(6)-E(6)^(-1))/(2*i);;
A:=[[0,0,co,-si],
[-si,co,0,0],
[co,si,0,0],
[0,0,si,co]];;
S:=[[1,0,0,0],
[0,1,0,0],
[0,0,-1,0],
[0,0,0,-1]];;
G:=Group(A,S);;

and 2 groups H and K

H:=Group(A^2,S*A^2*S);
K:=Group(A^3*S,S);
inn1:=InnerAutomorphism(G,A^3*S);
Inn1:=RestrictedMapping( inn1, H );
inn2:=InnerAutomorphism(G,S);
Inn2:=RestrictedMapping( inn2, H );
h:=DirectProduct(Group((1,2,3)),Group((1,2,3)));
isom:=IsomorphismGroups( H,h );
au:=AutomorphismGroup(h);
In1:=InverseGeneralMapping(isom)*Inn1*isom;
In2:=InverseGeneralMapping(isom)*Inn2*isom;
alpha:=GroupHomomorphismByImages(K,au,[A^3*S,S],[In1,In2]);

alpha is an homomorphism of K into h so I can compute the semi-direct
product of K and h but if I ask

SemidirectProduct(K,alpha,h);

I obtain an error message. Where is the error?

Thanks, Nicola.

--------------EAC4D3A17EBEE52EB2BB05A1
Content-Type: text/html; charset=us-ascii
Content-Transfer-Encoding: 7bit

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
<i>Dear Gap-forum,</i><i></i>
<p><i>I have 2 matrix A and S defined in this way</i>
<p>e:=CyclotomicField( 12 );;
<br>idm:=IdentityMat(4,e);;
<br>i:=E(4);;
<br>co:=(E(6)+(E(6))^(-1))/2;;
<br>si:=(E(6)-E(6)^(-1))/(2*i);;
<br>A:=[[0,0,co,-si],
<br>[-si,co,0,0],
<br>[co,si,0,0],
<br>[0,0,si,co]];;
<br>S:=[[1,0,0,0],
<br>[0,1,0,0],
<br>[0,0,-1,0],
<br>[0,0,0,-1]];;
<br>G:=Group(A,S);;
<br>&nbsp;
<br>&nbsp;<i></i>
<p><i>and 2 groups H and K</i>
<br>&nbsp;
<br>&nbsp;
<br>&nbsp;
<p>H:=Group(A^2,S*A^2*S);
<br>K:=Group(A^3*S,S);
<br>inn1:=InnerAutomorphism(G,A^3*S);
<br>Inn1:=RestrictedMapping( inn1, H );
<br>inn2:=InnerAutomorphism(G,S);
<br>Inn2:=RestrictedMapping( inn2, H );
<br>h:=DirectProduct(Group((1,2,3)),Group((1,2,3)));
<br>isom:=IsomorphismGroups( H,h );
<br>au:=AutomorphismGroup(h);
<br>In1:=InverseGeneralMapping(isom)*Inn1*isom;
<br>In2:=InverseGeneralMapping(isom)*Inn2*isom;
<br>alpha:=GroupHomomorphismByImages(K,au,[A^3*S,S],[In1,In2]);
<br>&nbsp;
<br>&nbsp;
<p><i>alpha is an homomorphism of K into h so I can compute the semi-direct
product of K and h but if I ask</i>
<br>&nbsp;
<p>SemidirectProduct(K,alpha,h);
<br>&nbsp;
<p><i>I obtain an error message. Where is the error?</i><i></i>
<p><i>Thanks, Nicola.</i></html>

--------------EAC4D3A17EBEE52EB2BB05A1--

> < [top]