Some properties of Umar semigroups: isomorphism theorems, ranks and maximal inverse subsemigroups

Abstract

© 2018 Springer Science+Business Media, LLC, part of Springer Nature In a paper published in 1994, Umar defined an interesting class of transformation semigroups which naturally generalizes the Vagner one-point completion of the symmetric inverse semigroup. In this paper we prove some isomorphism theorems for finite such semigroups and compute their ranks. Moreover, we determine all maximal inverse subsemigroups of an arbitrary transformation semigroup of this type which is not inverse.