# Math Help - cyclic or isomorphic

1. ## 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.

2. Originally Posted by apple2009
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 $S_4$?