Let S be a subsemigroup of a semigroup T and let IG(E) and IG(F) be the free idempotent generated semigroups over the biordered sets of idempotents of E of S and F of T, respectively. We examine the relationship between IG(E) and IG(F), including the case where S is a retract of T. We give suﬃcient conditions satisfied by T and S such that for any e∈E, the maximal subgroup of IG(E) with identity e is isomorphic to the corresponding maximal subgroup of IG(F). We then apply this result to some special cases and, in particular, to that of the partial endomorphism monoid PEnd A and the endomorphism monoid EndA of an independence algebra A of finite rank. As a corollary, we obtain Dolinka’s reduction result for the case where A is a finite set.
Bibliographical noteFunding Information:
The research was supported by Grants No. 11501430 of the National Natural Science Foundation of China, and by Grants No. JB150705 and No. XJS063 of the Fundamental Research Funds for the Central Universities, and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and by Grant No. 2016JQ1001 of the Natural Science Foundation of Shaanxi Province.
© 2017 Taylor & Francis.
- Biordered set
- free G-act
- independence algebra
- partial endomorphism