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My text explains it as: G1+G2+...+Gn ={(g1,g2,...gn)}|giEGi}, where (g1,g2,...,gn)(g'1,g'2,...,g'n) is defined as (g1g'1, g2g'2,..., gng'n). It then gives this as an example: U(8)+U(10) = {(1,1),(1,3),(1,7),(1,9),(3,1),(3,3),(3,7),(3,9),(5,1),(5,3),(5,7),(5,9),(7,1),(7,3),(7,7),(7,9)} . Since U(8)={1,3,5,7} and U(10)={1,3,7,9} doesn't this example have the form of (g1g'1, g1g'2, g1g'3, g1g'4, g2g'1, g2g'2, g2g'3.... and so forth until we cycled through it all)