A survey on Basic polygroups and their automorphisms

Document Type : Research Paper

Author

Department of Mathematies, National University of Skills (NUS), Tehran, Iran

Abstract

Polygroups have been applied in many area, such as geometry, lattices, combinatorics and color scheme. In this paper, we study a special type of polygroups; basic polygroups and present some of their properties. First, we determine the finite basic polygroup. We define the concept of characteristic by using the automorphism of a polygroup and prove that the basic set is a characteristic subpolygroup. A connection between basic polygroups associated with basic set is also investigated. The article provides valuable examples and results for researchers who study polygroups.

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References

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[3] B. Davvaz, Applications of the γ∗-relation to polygroups, Comm. Algebra, 35 no. 9 (2007) 2698–2706.
[4] B. Davvaz, A survey on polygroups and their properties, Proceedings of the International Conference on Algebra 2010, World Sci. Publ., Hackensack, NJ, (2012) 148–156.
[5] A. Mosayebi Dorcheh, k-nilpotent groups based on hypergroups, J. Algebr. Hyperstruct. Log. Algebras, 2 no. 2 (2021) 61–72.
[6] A. Mosayebi Dorcheh, On autosolvable and autonilpotent polygroups, J. Algebr. Hyperstruct. Log. Algebras, 2 no. 4 (2021) 39–49
Mathematics and Society
Volume 10, Issue 3 - Serial Number 3
September 2025
Pages 1-22

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History

  • Receive Date: 07 February 2024
  • Revise Date: 20 September 2024
  • Accept Date: 26 November 2024
  • Publish Date: 22 November 2025

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