Normal Hair

Recently I've been studying for the qualifying exam in algebra, which I will be taking on Wednesday. However, as a result of the excessive studying, my dreams have been affected. Several dreams last night reflected some math stuff.

In the first, and less exciting of the two I will share, I was going to a pizza place with a few friends. I was on the other side of the street and it was taking forever. I took a very roundabout way of getting there. Once I finally met up with my friends again, we concluded that I had merely proved something more than I needed to, but it still worked.

In the other dream, I was the target of a serial killer. This killer went around killing people with normal hair. I was at my apartment when a detective came in and asked if I had normal hair, to determine if I was in danger or not. Well, how did he determine if my hair was normal? He conjugated it! As he was conugating it, another detective came in, saw what was going on, and then there was some ordeal about the first really being the killer... don't know, don't care. Anyways, what you're really interested in:

The Mathematics Involved...
Given a group G with a subgroup H in G, we say that H is normal in G if for every g in G, we have gHg^-1=H. That is to say, for any g in G and for any h in H, we have ghg^-1 is an element of H. Multiplying on either side by g and g^-1 is called conjugating, which is a primary method of seeing if a subgroup is normal or not.