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.
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 ?
Last edited by NonCommAlg; Nov 30th 2009 at 04:30 AM.