Stable Quasiorderings on Some Permutable Inverse Monoids
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.
English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 4, pp 499-513.
Citation Example: Derech V. D. Stable Quasiorderings on Some Permutable Inverse Monoids // Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 445–457.