I have a question I was hoping for help on:
Prove or disprove every nonabelian group of order divisible by 6 contains a subgroup of order 6
I would guess that this statement is true based on a few examples I've done, but I have no idea why (or if it really is true). If I had a guess there might be some sort of isomorphism that I can relate non abelian groups of order 6 to. Would someone be able to help me? If you wouldn't mind, if you can help me, provide a simplistic explanation so that I may understand better. Thanks in advance for your help, I really appreciate it!