The inverse semigroup of all fence-preserving injections and its maximal subsemigroups
In this paper, we study the inverse semigroup \(IF_{n}\) of all partial injections \(\alpha\) on an \(n\)-element set such that both \(\alpha\) and \(\alpha^{-1}\) are fence-preserving (preserve the zig-zag order). The main result of this paper is the characterization of the maximal subsemigroups of...
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| Date: | 2025 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2025
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2353 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | In this paper, we study the inverse semigroup \(IF_{n}\) of all partial injections \(\alpha\) on an \(n\)-element set such that both \(\alpha\) and \(\alpha^{-1}\) are fence-preserving (preserve the zig-zag order). The main result of this paper is the characterization of the maximal subsemigroups of \(IF_{n}\): There are five types of maximal subsemigroups, whenever \(n\) is odd; if \(n\) is even, then the maximal semigroups are of the form \(IF_{n}\setminus \{\alpha \}\), where \(\alpha\) belongs to the least generating set of \(IF_{n}\). Moreover, we describe the i-conjugate elements in \(IF_{n}\). |
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