Finitely approximable regular semigroups

In this note it is proved that a regular semigroup whose subgroups are all finitely approximable is finitely approximable and that the set of idempotents of each principal factor is finite. As a corollary necessary and sufficient conditions are found for certain classes of regular semigroups to be finitely approximable.Translated from Matematicheskie Zametki, Vol. 17, No. 3, pp. 423–432, March, 1975.The author is grateful to L. N. Shevrin and Yu. N. Mukhin for their valuable observations and helpful discussions.