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

### 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

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 68, no. 11, Nov. 2016, pp. 1571-8, https://umj.imath.kiev.ua/index.php/umj/article/view/1943.

Issue

Section

Short communications