Generalised Tits alternative for linear semigroups Original Research Article

It is shown that a finitely generated linear semigroup T subset of or equal to GL(n, K) with no free non-commutative subsemigroups generates a nilpotent-by-finite subgroup of GL(n, K). This extends the results of Tits and Rosenblatt on finitely generated linear and finitely generated solvable groups. We use it to derive a ‘generalised Tits alternative’ for an arbitrary linear semigroup S subset of or equal to M (n, K) and to obtain consequences for the structure of the Zariski and strongly π-regular closures of such S.