Geodesic
A Generalization of an Addition Theorem for Solvable Groups
Canadian journal of mathematics, Tome 36 (1984) no. 3, pp. 529-536

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The “sets” in this paper are actually multi-sets. That is, we allow an element to occur several times in a set and distinguish between the number of elements in a set and the number of distinct elements in the set. On the few occasions when we need to avoid repetition we will use the term “ordinary set.“ Definition. Let G be a group and let S a set of elements of G. An r-sum in S is an ordered subset of S of cardinality r; the result of that r-sum is the product of its elements in the designated order. Definition. If S is a set, r(x, S) denotes the number of times x appears in S and [x, S] is a set consisting of r(x, S) copies of x. An n-set or n-subset is a set consisting of n elements. Hence [x, S] is an r(x, S)-subset of S. 
Yuster, Thomas; Peterson, Bruce. A Generalization of an Addition Theorem for Solvable Groups. Canadian journal of mathematics, Tome 36 (1984) no. 3, pp. 529-536. doi: 10.4153/CJM-1984-032-x
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