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The document defines and provides examples of "carry groups", which are Abelian groups formed by taking the Cartesian product of a group H (such as Z) with finite cyclic groups Zn and introducing a non-standard addition operation that allows carrying between coordinates. Specifically, 1 is carried from the ith coordinate into H whenever the sum of the ith coordinates exceeds the modulus ni. Finite and infinite carry groups are defined. Properties such as inverses and powers of elements in these groups are a

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