Complete classification of finite semigroups for which the inverse monoid of local automorphisms is a permutable semigroup

  • V. D. Derech

Abstract

A semigroup $S$ is called permutable if $\rho \circ \sigma = \sigma \circ \rho$. for any pair of congruences $\rho, \sigma$ on $S$. A local automorphism of semigroup $S$ is defined as an isomorphism between two of its subsemigroups. The set of all local automorphisms of the semigroup $S$ with respect to an ordinary operation of composition of binary relations forms an inverse monoid of local automorphisms. We present a complete classification of finite semigroups for which the inverse monoid of local automorphisms is permutable.
Published
25.11.2016
How to Cite
Derech, V. D. “Complete Classification of Finite Semigroups for Which the Inverse Monoid of local Automorphisms Is a Permutable Semigroup”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 11, Nov. 2016, pp. 1571-8, http://umj.imath.kiev.ua/index.php/umj/article/view/1943.
Section
Short communications