My Math Forum Prove H is a normal subgroup of G

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 March 23rd, 2015, 03:13 PM #1 Newbie   Joined: Feb 2015 From: Alabama Posts: 3 Thanks: 0 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.
 March 25th, 2015, 03:34 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 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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