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Endomorphisms of Cayley digraphs of rectangular groups
Let \(\mathrm{Cay}(S,A)\) denote the Cayley digraph of the semigroup \(S\) with respect to the set \(A\), where \(A\) is any subset of \(S\). The function \(f : \mathrm{Cay}(S,A) \to \mathrm{Cay}(S,A)\) is called an endomorphism of \(\mathrm{Cay}(S,A)\) if for each \((x,y) \in E(\mathrm{Cay}(S,A))\)...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2019
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/388 |
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| Summary: | Let \(\mathrm{Cay}(S,A)\) denote the Cayley digraph of the semigroup \(S\) with respect to the set \(A\), where \(A\) is any subset of \(S\). The function \(f : \mathrm{Cay}(S,A) \to \mathrm{Cay}(S,A)\) is called an endomorphism of \(\mathrm{Cay}(S,A)\) if for each \((x,y) \in E(\mathrm{Cay}(S,A))\) implies \((f(x),f(y)) \in E(\mathrm{Cay}(S,A))\) as well, where \(E(\mathrm{Cay}(S,A))\) is an arc set of \(\mathrm{Cay}(S,A)\). We characterize the endomorphisms of Cayley digraphs of rectangular groups \(G\times L\times R\), where the connection sets are in the form of \(A=K\times P\times T\). |
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