Periodic Elements of the Free Idempotent Generated Semigroup on a Biordered Set

We show that every periodic element of the free idempotent generated semigroup on an arbitrary biordered set belongs to a subgroup of the semigroup. © 2010 World Scientific Publishing Company.The second author was supported in part by the NSF grant DMS-0700811 and by a BSF (USA-Israeli) grant. The third author acknowledges support from the Russian Foundation for Basic Research, grant 09-01-12142, and from the Federal Education Agency of Russia, grant 2.1.1/3537