The pre-periods of all endomorphisms of a finite cyclic group
Aveya Charoenpolaveya.ch@rmuti.ac.thDivision of MathematicsFaculty of EngineeringRajamangala University of TechnologyIsan Khonkaen Campus, 40000, ThailandView full profile → , Napaporn Sarasitnapaporn.sr@rmuti.ac.thDivision of MathematicsFaculty of EngineeringRajamangala University of TechnologyIsan Khonkaen Campus, 40000, ThailandView full profile → , Pongsaphat Prachumdangpong_sa_phat@kkumail.comDepartment of MathematicsFaculty of ScienceKhon Kaen University40002, ThailandView full profile → , *Udom ChotwattakawanitCorresponding authorudomch@kku.ac.thDepartment of MathematicsFaculty of ScienceKhon Kaen University40002, ThailandView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Nov 2024
- Published Online:
- 14 Aug 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2293
- Pages:
- 2351–2357
Abstract
Keywords
Subject Classifications
References
[1] G. Fang and J. Fang, “The strong endomorphism kernel property in distributive p-algebras.” Southeast Asian Bulletin of Mathematics, vol. 37, no. 4 (2013).
[2] Y. Susanti and J. Koppitz, “On endomorphisms of power-semigroups,” Asian-European Journal of Mathematics, vol. 10, no. 03, p. 1750058 (2017).
[3] M. Böttcher and U. Knauer, “Endomorphism spectra of graphs,” Discrete Mathematics, vol. 109, no. 1-3, pp. 45--57 (1992).
[4] U. Knauer, “Endomorphism types of trees,” Words, Languages, and Combinatorics, World Scientific, Singapore, pp. 273-287 (1992).
[5] K. Grant, R. Nowakowski, and I. Rival, “The endomorphism spectrum of an ordered set,” Order, vol. 12, pp. 45-55 (1995).
[6] J. Konieczny, “Automorphism groups of endomorphism monoids of free g-sets,” Asian-European Journal of Mathematics, vol. 7, no. 01, p. 1450015 (2014).
[7] H. Ghumashyan and J. Guric ̆an, “Endomorphism kernel property for finite groups,” Mathematica Bohemica, vol. 147, no. 3, pp. 347-358 (2022).
[8] J. Fang and Z. J. Sun, “Finite abelian groups with the strong endomorphism kernel property,” Acta Mathematica Sinica, English Series, vol. 36, pp. 1076-1082 (2020).
[9] M. Sha, “Digraphs from endomorphisms of finite cyclic groups,” J. Combin. Math. Combin. Comp, vol. 83, p. 105-120 (2012).
[10] K. Denecke and C. Ratanaprasert, “N-ary operations with long pre-periods,” Asian-European Journal of Mathematics, vol. 2, no. 02, pp. 201--212 (2009).
[11] C. Ratanaprasert and K. Denecke, “Unary operations with long pre-periods,” Discrete Mathematics, vol. 308, pp. 4998-5005 (2008).
[12] D. Zupnik, “Cayley functions,” in Semigroup Forum, vol. 3, pp. 349--358 (1971).
[13] N. Jacobson, “Basic algebra ii: Second edition, (2009).
[14] E. Halušková, “Strong endomorphism kernel property for monounary algebras,” Mathematica Bohemica, vol. 143, no. 2, pp. 161-171 (2018).
[15] I. Pozdnyakova, “Semigroups of endomorphisms of some infinite monounary algebras,” Journal of Mathematical Sciences, vol. 190, no. 5, pp. 658--668 (2013).
[16] U. Ahmad, “The power digraphs associated with generalized dihedral groups,” Discrete Mathematics, Algorithms and Applications, vol. 7, no. 04, p. 1550057 (2015).
[17] E. Brown, “Directed graphs defined by arithmetic (mod n),” Fibonacci Quarterly, vol. 35, pp. 346-351 (1997).
[18] M. H. Mateen, M. K. Mahmmod, D. Alghazzawi, and J.-B. Liu, “Structures of power digraphs over the congruence equation xp ≡ y (mod m) and enumerations,” AIMS Math, vol. 6, no. 5, pp. 4581-4596 (2021).
[19] U. Ahmad and H. Syed, “On the heights of power digraphs modulo n,” Czechoslovak mathematical journal, vol. 62, pp. 541--556 (2012).
[20] D. Jakubikova-Studenovska and J. Pócs, Monounary algebras (2009).
[21] A. Charoenpol and U. Chotwattakawanit, “The pre-period of the glued sum of finite modular lattices.” Discussiones Mathematicae: General Algebra & Applications, vol. 43, no. 2, pp. 223-231 (2023).
[22] A. Charoenpol and U. Chotwattakawanit, “The maximum pre-period property of the direct product of chains,” Asian-European Journal of Mathematics, vol. 16, no. 09, p. 2350155 (2023).
