Question: Let (G, ) be a group where x a y = b a c = x y = b

Let (G, ◦) be a group where
x ◦ a ◦ y = b ◦ a ◦ c = x ◦ y = b ◦ c,
for all a, b, c, x, y ∈ G. Prove that (G, ◦) is an abelian group.

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