1. The hardest part of this reading to understand is theorem 8.15, which is the second sylow theorem. I do not know how if P and K are both Sylow's how P = (x^-1)Kx for some x in G. I do know see how that would work and it does not make much sense. Can't P and K just be differnt prime number-subgroups, so then they would not be related in that way? I'm confused.
2. The most interesting part of this reading was that there was such a classification as a Sylow p-subgroup. I like when new properties and terminologies are introduced to us. It makes me feel like people have really studied abstract algebra before us and have created the most important things you can do with groups so that I know these things are important and are not just random theorems and properties to random groups of numbers. So I like this and I like new things like Sylow p-subgroups and that is what I find so interesting about this section.
No comments:
Post a Comment