Is U-8 abelian?
Because U(8) is an Abelian group, it suffices to check followings: φ(32) = φ(1) = 1 = 112 = φ(3)2, φ(52) = φ(1) = 1 = 52 = φ(5)2, φ(72) = φ(1) = 1 = 72 = φ(7)2, φ(3 · 5) = φ(7) = 7 = 11 · 5 = φ(3) · φ(5), φ(3 · 7) = φ(5) = 5 = 11 · 7 = φ(3) · φ(7), φ(5 · 7) = φ(3) = 11 = 5 · 7 = φ(5) · φ(7).
Because U(8) is an Abelian group, it suffices to check followings: φ(32) = φ(1) = 1 = 112 = φ(3)2, φ(52) = φ(1) = 1 = 52 = φ(5)2, φ(72) = φ(1) = 1 = 72 = φ(7)2, φ(3 · 5) = φ(7) = 7 = 11 · 5 = φ(3) · φ(5), φ(3 · 7) = φ(5) = 5 = 11 · 7 = φ(3) · φ(7), φ(5 · 7) = φ(3) = 11 = 5 · 7 = φ(5) · φ(7).
