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The Attempt at a Solution
Well thankfully I just have to present closure under mult. inverses and closure under addition. But I seem to be going in circles...if a is in G, then we need to show that a^{1} is also in G.
So a*a^{1} = 1_{F}, but is a^{1} in G...so we can write a = a^{p}, then if we can write a^{1} = (a^{p})^{1}, then we'll be good. But how the heck do I do that?
For closure under addition, I'm not really sure how to use the binomial theorem here, since we know that a + b means we can write them both as a^{p} + b^{p}, and now we've got to show that a^{p} + b^{p} can be written as (α + β)^{p}. Not sure how to get this one started either.
Any help is appreciated, thanks in advance.
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