Subgroups of free idempotent generated semigroups: full linear monoid

Abstract

We develop some new topological tools to study maximal subgroups of free idempotent generated semigroups. As an application, we show that the rank 1 component of the free idempotent generated semigroup of the biordered set of a full matrix monoid of n x n matrices, n>2$ over a division ring Q has maximal subgroup isomorphic to the multiplicative subgroup of Q.

We hope to use similar methods to study the higher rank components

References in corpus (1)

• Periodic elements of the free idempotent generated semigroup on a biordered set

Cited by in corpus (7)

• Maximal subgroups of free idempotent generated semigroups over the full transformation monoid
• Maximal subgroups of free idempotent generated semigroups over the full linear monoid
• Free idempotent generated semigroups and endomorphism monoids of free $G$-acts
• Free idempotent generated semigroups over bands
• Every group is the maximal subgroup of a naturally occurring free idempotent generated semigroup
• Presentations for singular wreath products
• The mathematical work of K.S.S. Nambooripad