Let G be a group. For any element g of G, define gZ(G) =
Chapter 8, Problem 9SE(choose chapter or problem)
Let G be a group. For any element g of G, define gZ(G) = {gh | h ? Z(G)}. If a is an element of G of order 4, prove that H = Z(G) x aZ(G) x a2Z(G) x a3Z(G) is a subgroup of G. Generalize to the case that |a| = k.
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