Commutators-based graph in polygroup
In this paper, first, we study commutators of a polygroup. Then for a finite polygroup $P$ and a fixed element $g \in P$, we introduce the $g$-graph $\Delta_P^g$. In addition, with some additional conditions, we see that it is connected and the diameter is at most $3$. Then, we investigate isomorphi...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2024-12-01
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| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_4113_fde3440e891e2208b2ef62719b472b20.pdf |
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| Summary: | In this paper, first, we study commutators of a polygroup. Then for a finite polygroup $P$ and a fixed element $g \in P$, we introduce the $g$-graph $\Delta_P^g$. In addition, with some additional conditions, we see that it is connected and the diameter is at most $3$. Then, we investigate isomorphic graphs. Specially, we obtain a new isomorphic graph derived from an isomorphic graph and two non-commutative isomorphic polygroups. Also, we show that two polygroups with isomorphic graphs preserve nilpotency. |
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| ISSN: | 2251-7952 2645-4505 |