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

Abstract

We show that the rank r r component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of n × n n \times n matrices over a division ring Q Q has maximal subgroup isomorphic to the general linear group G L r ( Q ) GL_r(Q) , where n n and r r are positive integers with r > n / 3 r > n/3 .