Let $G$ be a finite group and let $k$ be a finite field of characteristic $p>0$ such that $p\mid |G|$.
Let $M_1, M_2$ and $M_3$ be finitely generated $kG$-modules.
I read in the MAGMA online manual that MAGMA can compute pullbacks, but the function provided there works for the input types ModAlg and ModAlgFldElt, respectively.
Unfortunately, I was not able to let MAGMA compute a pullback when given two $kG$ homomorphisms $f: M_1\rightarrow M_3$ and $g: M_2\rightarrow M_3$.
Therefore, I'd like to ask:
Can MAGMA compute pullbacks of $kG$-modules?
Thanks for the help.
EDIT (April 7th 2020):
I tried the following, but got an error message.
> G:=Alt(4);
> K:=GF(4);
> PIMs:=ProjectiveIndecomposableModules(G,K);
> P1:=PIMs[1];
> P2:=PIMs[2];
> P3:=PIMs[3];
>
>
> h:=Random(GHom(P1,P3));
> h;
[ 1 K.1^2 K.1 0]
[K.1^2 1 1 K.1^2]
[ K.1 0 K.1^2 1]
[ 0 K.1 0 K.1]
>
>
> k:=Random(GHom(P2,P3));
> k;
[K.1^2 K.1^2 1 1]
[ 1 K.1^2 K.1^2 K.1]
[ K.1 K.1^2 0 K.1^2]
[ 1 K.1^2 K.1^2 K.1]
>
> M,i,j,p,q:=DirectSum(P1,P2);
> h*p;
>> h*p;
^
Runtime error in '*': Bad argument types
Argument types given: ModMatGrpElt[FldFin], Map[ModGrp, ModGrp]