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Math Help - cyclic or isomorphic

  1. #1
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    cyclic or isomorphic

    Let G be a group with |G|=4. Define the map Λ: G→Sym(G) by Λ(g)(x)=g o x for all g in the group G and all x in the set G. Prove: Either G is cyclic or G is isomorphic to V₄.
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  2. #2
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    Quote Originally Posted by apple2009 View Post
    Let G be a group with |G|=4. Define the map Λ: G→Sym(G) by Λ(g)(x)=g o x for all g in the group G and all x in the set G. Prove: Either G is cyclic or G is isomorphic to V₄.
    your map, \Lambda, is injective. so G can be considered as a subgroup of \text{Sym}(G) \cong S_4. now what are the subgroups of order 4 in S_4?
    Last edited by NonCommAlg; November 30th 2009 at 03:30 AM.
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