Free idempotent generated semigroups and endomorphism monoids of independence algebras

We study maximal subgroups of the free idempotent generated semigroup where E is the biordered set of idempotents of the endomorphism monoid of an independence algebra , in the case where has no constants and has finite rank n. It is shown that when the maximal subgroup of containing a rank 1 idempotent is isomorphic to the corresponding maximal subgroup of containing . The latter is the group of all unary term operations of . Note that the class of independence algebras with no constants includes sets, free group acts and affine algebras.