The normal subgroup of a normal subgroup need not be normal in the original group (normalcy is not transitive). Could somebody provide me with an example of where this is the case? Thanks :D
They are simple for ##n > 4## (and three). "Simple in" is a bit of a weird wording.Small symmetry groups.... Is the Alternating symmetry group (A_n) always simple in S_n?
If you consider a whole symmetric group it might be more difficult to prove because you have an additional transposition at hand to get closure under conjugation.If not that's the route i'm going to go.... It's always normal because the index in S_n is always going to be two obviously... Anyway if I find a normal subgroup of some A_n maybe it won't be normal in S_n? Do you think this is a smart route to take?