TY - JOUR AU - V. D. Derech PY - 2014/04/25 Y2 - 2024/03/28 TI - Stable Quasiorderings on Some Permutable Inverse Monoids JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 66 IS - 4 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2147 AB - 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. ER -