[GAP Forum] central product

[sumeyra uskudar]

Actually, the function turned out to be inconsistent unfortunately.
Can it be checked once again?
Or any other comments for the central product?

2012/5/13 Benjamin Sambale <benjamin.sambale at gmail.com>

> Hi,
>
> some time ago I wrote the following function just for myself:
>
> CentralProduct:=function(arg)
> local G,H,D,f,f1,f2,S,g,M;
> if Length(arg)=1 and IsList(arg[1]) then arg:=arg[1]; fi;
> if Length(arg)=0 then return TrivialGroup(); fi;
> if Length(arg)=1 then return arg[1]; fi;
> G:=arg[1];
> H:=arg[2];
> D:=DirectProduct(G,H);
> f:=IsomorphismGroups(Center(G),Center(H));
> if f=fail then
>    if IsPGroup(Center(G)) and IsCyclic(Center(H)) then
>
>  f:=IsomorphismGroups(Center(G),Filtered(Subgroups(Center(H)),M->Size(M)=Size(Center(G)))[1]);
>        if f=fail then Error("Centers are not compatible"); fi;
>    else
>
>  f:=IsomorphismGroups(Filtered(Subgroups(Center(G)),M->Size(M)=Size(Center(H)))[1],Center(H));
>        if f=fail then Error("Centers are not compatible"); fi;
>    fi;
> fi;
> f1:=Embedding(D,1);
> f2:=Embedding(D,2);
> S:=Set(Center(G),g->g^(f1)*(g^(-1))^(f*f2));
> Remove(arg,1);
> arg[1]:=FactorGroup(D,Subgroup(D,S));
> return CentralProduct(arg);
> end;
>
> No warranty!
>
> Best wishes,
> Benjamin
>
> Am 12.05.2012 12:36, schrieb sumeyra uskudar:
>
>  Dear forum,
>>
>> Is there a way to define a central product in GAP, and how do we define
>> the
>> common central factor in this function?
>> For example we want to define G:=Q8.K(the central product),
>> where, Q8 is the quaternion group of order 8 presented as ;
>> <a,b:a^4=1,b^2=a^2,bab^-1=a^-1>
>> and K=<x,y:x^4=y^4=1,yxy^-1=x^-1>
>> with te common central factor being x^2y^2.
>>
>> Thanks in advance,
>>
>>


-- 
*Sümeyra Bedir*