Question

Exercise3.7.6 Prove that for all n≥2,we have Sn≌An为Z2,where Sn is the symmetric group and Anthe alternating subgroup (consisting of the even permutations).Hint:use Proposition 3.7.7.You have to find asubgroup K Sn with

KZ2 (c.f.Erample 3.7.8).

Fig: 1