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 th...
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| Date: | 2014 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2014
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2147 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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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