Hello everyone. In a recent post a member asked this question
.Let be a prime and . Prove that if is a group with that contains an element with
TheEmptySet provided a solution that was of course satisfactory, but I came up with an alternative proof. Now the proof seems "too simple" and I am moderately sure I made a fatal assumption. Can someone validate this?
Proof: Let . If we are done, otherwise by Lagrange's theorem for . But this would mean that and since this subgroup is cyclic and wouldn't this mean that there is some such that and ?