Finite cyclic q-group’s automorphisms with qr -generator
DOI:
https://doi.org/10.15282/daam.v5i1.10970Keywords:
Cyclic group, Automorphism group, Generator, Compatible action , Number theoryAbstract
The finite cyclic q-group, where q being odd prime, requires generators to validate the formation of automorphisms. A summary of cyclic groups, automorphisms, and characteristics is provided as a foundation for this research. By evaluating the automorphisms, the generators for the qr -power cyclic group in their specific sequence have been uncovered and presented as the key finding.
References
[1]Brown R, Loday JL. Excision homotopique en basse dimension. Comptes Rendus de l'Académie des Sciences - SeriesI - Mathematics. 1984;298(15):353-56.
[2]Brown R, Johnson DL, Roberson EF. Some computations of non-abelian tensor products of groups. Journal ofAlgebra. 1987;11(1):177-202.
[3]Dummit DS, Foote RM. Abstract Algebra. 3rd ed. Hoboken, NJ: Wiley; 2003.
[4]Clark WE. Elementary Abstract Algebra. Retrieved fromhttps://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Elementary_Abstract Algebra_(Clark); 2021.
[5]Broche O, García-Lucas D, Del Rio A. A classification of the finite 2-generator cyclic-by-abelian groups of prime-power order. International Journal of Algebra and Computation. 2023;33(04):641-86.
[6]Miech RJ. On p-groups with a cyclic commutator subgroup. Journal of the Australian Mathematical Society.1975;20(2):178-98.
[7]Song Q. Finite two-generator p-groups with cyclic derived group. Communications in Algebra. 2013;41(4):1499-513.
[8]Mohamad MS. Compatibility conditions and nonabelian tensor products of finite cyclic groups of p-power order. PhDThesis. Malaysia: Universiti Teknologi Malaysia, 2012.
[9]Shahoodh MK. Compatible Pair of Actions for Finite Cyclic Groups of p-Power Order. PhD Thesis. Malaysia:Universiti Malaysia Pahang, 2018.
[10]Lachaud G. The Klein quartic as a cyclic group generator. Moscow Mathematical Journal. 2005;5:857-68.
[11]Sander JW, Sander T. The Klein quartic as a cyclic group generator. Moscow MathematicalJournal. 2013;133(2):705-18.
[12]Gopalakrishnan M, Kumari NNM. Generator graphs for cyclic groups. AIP Conference Proceedings. 2019 June;2112(1):020119.
[13]Villeta RB, Castillano EC, Padua RN. On the generators of the group of units modulo a prime and its analytic andprobabilistic view. Recoletos Multidisciplinary Research Journal. 2021;9(2):115-21.
[14]Tanaka Y. Average probability of an element being a generator in the cyclic group. American Journal ofComputational Mathematics. 2023;13(2):230-235.
[15]Sommer-Simpson J. Automorphism Groups for Semidirect Products of Cyclic Groups. arXiv preprint. 2019;arXiv:1906.05901.
[16]Alperin J. Groups with finitely many automorphisms. Pacific Journal of Mathematics. 1962;12(1):1-5.
[17]Baer R. Finite extensions of abelian groups with minimum condition. Transactions of the American MathematicalSociety. 1955;79(2):521-40.
[18]Ahmad S. Cycle structure of automorphisms of finite cyclic groups. Journal of Combinatorial Theory.1969;6(4):370-74.
[19]Emery S. About Automorphisms of Some Finite Groups. Master Thesis. United States: West Chester University,2021.
[20]Groups, Algorithm, and Programming (GAP) Software. Retrieved from https://www.gap-system.org/; 2024.
[21]Burton D. Elementary Number Theory. 6th ed. USA: McGraw Hill; 2005.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 The Author(s)

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.