Thanks for your help. The hint for the first one was a good step in the right direction.
One the second one, I've made progress, but I could use a bit of clarification on two points.
-First, to show that G(m) is a subgroup of G one of the things I need to do is show that if A is in G(m) then...
Having trouble with a couple of algebra questions and would really appreciate any hints or pointers.
1. A is a subgroup of group G with a finite index. Show that
N = \bigcap_{x \in G}x^{-1}Ax
is a normal subgroup of finite index in G.
I'm able to show that N is a subgroup of G by applying the...
Hey guys, thanks for the tips. They really helped out. The one with xy and -yx was indeed really simple once I looked at it that way. Also the way the binomial expansion on the frobenius field problem canceled out was rather nifty.
I'm having trouble with what seemed like a trivial problem at first, but now I'm rather stuck. If R is a ring with xy=-yx for any x,y from the ring, xyz+xyz=0 must be true for any x,y,z from the ring. I'm trying to show why that is.
Letting y=x yields x^2+x^2=0. Thus then breaking it up into...