Semigroups of zero entropy Original Research Article

Let S be the multiplicative semigroup generated by a finite set {s1,…,sk} of n by n matrices over a field. For every positive integer m, let l(m) denote the number of sequences i1,…,im such that the corresponding product si1cdots, three dots, centeredsim is nonzero. We say that the entropy of S is zero if 0 is the limit of the sequence logl(m)/m. The structure of semigroups of entropy zero is described.