On the graph of the Maximal subgroup of the Cyclic Group
DOI:
https://doi.org/10.31642/JoKMC/2018/130104Keywords:
Maximal subgroup, Max graph, Cyclic groupAbstract
The maximal graph is a finite graph for any two vertices that are joined if is a maximal subgroup and is denoted by .In this paper, we will present an algorithm for calculating the graph of .Where we will study several cases of the value of so there will be an algorithm for each case. To calculate the maximum number of subgroups of the cyclic group . We’ll employ the Gap program. and use this to find some of the properties of the maximal graph.
Downloads
References
[1] W. H. Gustafson, What is the probability that two group elements commute?, Amer. Math. Monthly 80 (1973), 1031–1034.
[2] A. Erfanian, K. Moradipour, and N. H. Sarmin, Finite groups with the same commuting probability, Res. J. Appl. Sci. Eng. Technol. 5 (2013), no. 13, 3525–3528.
[3] M. S. Lazorec, Relative cyclic subgroup commutativity degrees of finite groups, Filomat 33 (2019), no. 13, 4021–4032.
[4] G. Chartrand and P. Zhang, Introduction to Graph Theory, Posts and Telecom Press, Beijing, China, 2006.
[5] D. W. Jensen and M. K. Keane, A number-theoretic approach to subgroups of dihedral groups, SUT J. Math. 37 (1990), no. 1, 1–12.
[6] D. B. West, Introduction to Graph Theory, Prentice-Hall of India Pvt. Ltd., New Delhi, 2003.
[7] G. James and M. Liebeck, Representations and Characters of Groups, 2nd ed., Cambridge University Press, New York, 2001.
[8] H. B. Shelash and A. R. Ashrafi, Wielandt subgroups of certain finite groups, Math. Notes 177 (2020), 121–131.
[9] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.8.9, 2019. https://www.gap-system.org
[10] J. M. Oh, Y. Kim, and K. W. Hwang, The number of chains of subgroups in the lattice of subgroups of the dicyclic group, Discrete Dyn. Nat. Soc. (2012), Art. ID 760246, 17 pp.
[11] C. Gary and P. Zhang, Introduction to Graph Theory, Posts and Telecom Press, Beijing, China, 2006.
[12] S.Naduvath, Lecture notes on Graph Theory, Published by Centre for Studies in Discrete Mathematics, Vidya Academy of Science Technology, Thrissur-680501, Kerala, India.http://www.csdm.org.in November 2017
Downloads
Published
Issue
Section
Categories
License
Copyright (c) 2026 Ohood A. Hadi, Hayder B. Shelash
This work is licensed under a Creative Commons Attribution 4.0 International License.
which allows users to copy, create extracts, abstracts, and new works from the Article, alter and revise the Article, and make commercial use of the Article (including reuse and/or resale of the Article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made and the licensor is not represented as endorsing the use made of the work.
How to Cite
