# Stable Quasiorderings on Some Permutable Inverse Monoids

### Abstract

Let*G*be an arbitrary group of bijections on a finite set. By

*I*(

*G*), we denote the set of all injections each of which is included in a bijection from

*G*. The set

*I*(

*G*) forms an inverse monoid with respect to the ordinary operation of composition of binary relations. We study different properties of the semi-group

*I*(

*G*). In particular, we establish necessary and sufficient conditions for the inverse monoid

*I*(

*G*) to be permutable (i.e.,

*ξ*○

*φ*=

*φ*○

*ξ*for any pair of congruences on

*I*(

*G*)). In this case, we describe the structure of each congruence on

*I*(

*G*). We also describe the stable orderings on

*I*(

*A*

_{ n }), where

*A*

_{ n }is an alternating group.

Published

25.04.2014

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 66, no. 4, Apr. 2014, pp. 445–457, https://umj.imath.kiev.ua/index.php/umj/article/view/2147.

Issue

Section

Research articles