On the growth of generating sets for direct powers of semigroups
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For a semigroup S its d-sequence is d(S) = (d1, d2, d3, . . .), where di is the smallest number of elements needed to generate the ith direct power of S. In this paper we present a number of facts concerning the type of growth d(S) can have when S is an infinite semigroup, comparing them with the corresponding known facts for infinite groups, and also for finite groups and semigroups.
Hyde , J T , Loughlin , N , Quick , M , Ruskuc , N & Wallis , A 2012 , ' On the growth of generating sets for direct powers of semigroups ' Semigroup Forum , vol 84 , no. 1 , pp. 116-130 . , 10.1007/s00233-011-9352-4
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