Let G be a group and H a subgroup. For any element g of G,
Chapter 3, Problem 76E(choose chapter or problem)
Problem 76E
Let G be a group and H a subgroup. For any element g of G, define gH = {gh | h ∈ H}. If G is Abelian and g has order 2, show that the set K = H ∪ gH is a subgroup of G. Is your proof valid if we drop the assumption that G is Abelian and let K = Z(G) ∪ gZ(G)?
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