abstact algebra If G is a group such that every one of its S

abstact algebra! If G is a group such that every one of its Sylow subgroups (for every prime p) is cyclic and normal, prove that G is a cyclic group

Solution

Let G bra group

Everyone of its slow subgroups

are cyclic

that is x, y belongs G then

xgx^-1,ygy^-1 belongs to normal groups

therefore slow subgroups of order p is cyclic

So G is agroup