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March 23rd, 2015, 03:13 PM   #1
msv
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Prove H is a normal subgroup of G

Let G be a group and suppose that k is a fixed natural number. Suppose that in G it is always the case that (ab)^k = (a^k)(b^k) for all a,b in G.
Let H = {a^k: a is in G}. (Thus H is the set of all k th powers). Prove FIRST that H is a subgroup of G and THEN that it is also normal in G.
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March 25th, 2015, 03:34 AM   #2
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The first part, of course, is almost trivial. What have you done to try to prove the subgroup is normal? What is the definition of "normal" subgroup?
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