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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 4, pp. 445–457, April, 2014.
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Derech, V.D. Stable Quasiorderings on Some Permutable Inverse Monoids. Ukr Math J 66, 499–513 (2014). https://doi.org/10.1007/s11253-014-0948-1
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DOI: https://doi.org/10.1007/s11253-014-0948-1