## ยง Normal subgroups through the lens of actions

- finite group is permutation subgroup
- ghg' is relavelling by g
- if gHg' = H, then H does not care about labelling
- thus H treats everyone uniformly
- prove that if H is normal, then if s in fix(H) then orb(s) in fix(H)
- when is stab(S) normal?when Stab(gx) equals g Stab(x) g' ?

- topology onS: closed sets are the common fixpoints of a set of group elements.