Stable Quasiorderings on Some Permutable Inverse Monoids
AbstractLet 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.
How to Cite
Derech, V. D. “Stable Quasiorderings on Some Permutable Inverse Monoids”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 4, Apr. 2014, pp. 445–457, http://umj.imath.kiev.ua/index.php/umj/article/view/2147.