Let $G$ be a finite group and $p$ be a prime.
Moreover, let $k$ be a finite field of characteristic $p$, such that $p$ divides $|G|$. Furthermore suppose that $k$ is a splitting field for $G$.
Let $M$ be a $kG$-module.
I wrote the following function in MAGMA and I am wondering what it does.
InverseRep:=function(M)
G:=Group(M);
f:=Representation(M);
return GModule(G, [(f(G.i))^-1: i in [1..Ngens(G)]]);
end function;
Why is no error message returned (since this is not well-defined because f_new$(g1\cdot g2)\neq$f_new$(g1)\cdot$f_new$(g2)$) ?
But the new rep. is a rep. for the opposite group.
Question:
Does MAGMA automatically recognize this and somehow identify $G$ and $G^\text{op}$?
Thank you very much for the help.