Thread: 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.

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, is injective. so can be considered as a subgroup of now what are the subgroups of order in ?