Prove that contains a subgroup isomorphic to for all being the alternating group of degree n and S the symmetric group. I really have no idea how to approach this and it's had me stumped for quite a while. Any help would be much appreciated.
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Originally Posted by Beaky Prove that contains a subgroup isomorphic to for all being the alternating group of degree n and S the symmetric group. I really have no idea how to approach this and it's had me stumped for quite a while. Any help would be much appreciated. Say acts on , and , and let be the transposition that interchanges n-1 and n . Define a map by Now show is a group monomorphism. Tonio
Ok thanks a lot. It seems obvious enough now, but I don't think I would have thought of that.
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