Maximal subgroups of free idempotent generated semigroups over the full linear monoid

Abstract

We show that the rank r component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of n × n matrices over a division ring Q has maximal subgroup isomorphic to the general linear group GLr(Q), where n and r are positive integers with r < n/3. © 2013 American Mathematical Society.