Maximal homomorphic group image and convergence of convolution sequences on a semigroup (Q1426851)

Let \(\mu\) be a probability measure on a locally compact semigroup \(S\) which is generated by \(\text{supp\,} p\). Assume that \((\mu^n)_{n\geq 1}\) is tight which is, for instance, the case for compact semigroups. The authors investigate the convergence of \(\mu^n\) in terms of the convergence of its homomorphic image on a factor group of the compact subgroup of \(S\) that appears in the Rees-Suschewitsch decomposition of a closed minimal ideal in \(S\). The results are then applied to matrix semigroups.