# Using Magma to Find a Fixed Points Module [closed]

Let $G$ be a group and $H$ a subgroup. Suppose $M$ is a $kN_G(H)$-module ($k$ a field). Then the $H$-fixed points in $M$ denoted $M^H$ is a $kN_G(H)$-module. Is there a way to access this module in Magma?

More specifically, it is easy enough to find $M^H$ by calling Fix(Restriction(M,H)). But is there any way to force Magma to consider this as a $kN_G(H)$-module, it only recognizes it as an $kH$-module.

## 1 Answer

This question is not about research level mathematics, so it is really not suitable for mathoverflow. But I'll answer it anyway. The code below works.

> G := Sym(6);
> H := sub< G | (1,2,3) >;
> N := Normalizer(G,H);
> M := PermutationModule(G, GF(7));
> MH := Restriction(M,H);
> MN := Restriction(M,N);
> FMH := Fix(MH);
> m := Morphism(FMH,MH);
> S := sub< MN |  [ m(FMH.i) : i in [1..Ngens(FMH)]] >;

• Dear @Derek Holt: If you think the question is not suitable, why not just leave a comment instead of an answer? It seems to me that an answer only legitimizes the question. – Ricardo Andrade Jun 19 '15 at 21:16
• @RicardoAndrade Yes you are right! I'll avoid doing that in future. – Derek Holt Jun 19 '15 at 22:39