Finite cyclic group of p-power order and its compatibility conditions

• Main Authors: Fatin Hanani, Hasan, Mohd Sham, Mohamad, Yuhani, Yusof, N.A., Mohd Busul Aklan
• Format: Article
• Language: English
• Published: Universiti Malaysia Pahang Publishing 2023
• Subjects: Q Science (General); QA Mathematics
• Online Access: http://umpir.ump.edu.my/id/eprint/41616/1/Finite%20cyclic%20group%20of%20p-power%20order%20and%20its%20compatibility%20conditions_Upload.pdf; http://umpir.ump.edu.my/id/eprint/41616/; https://doi.org/10.15282/daam.v4i2.10022; https://doi.org/10.15282/daam.v4i2.10022

Finite cyclic groups of p-power order, where p represents a prime number, have long been an interesting field of study in abstract algebra. This paper investigates the compatibility conditions that control their existence and behaviour. An overview of cyclic groups, automorphisms and their properties is given as groundwork for this research. By analysing the interaction between the group's order and its generator, we discovered the compatibility conditions and presented them as the primary finding in this paper.