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

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