{"id":10071,"date":"2024-12-02T06:35:02","date_gmt":"2024-12-02T06:35:02","guid":{"rendered":"https:\/\/icertpublication.com\/?page_id=10071"},"modified":"2026-03-07T07:22:08","modified_gmt":"2026-03-07T01:52:08","slug":"studying-the-computational-approaches-and-algorithms-for-calculating-the-generalized-commuting-probability-of-finite-group","status":"publish","type":"page","link":"https:\/\/icert.org.in\/index.php\/edu-mania\/edumania-vol-02-issue-04\/studying-the-computational-approaches-and-algorithms-for-calculating-the-generalized-commuting-probability-of-finite-group\/","title":{"rendered":"Studying The Computational Approaches And Algorithms For Calculating The Generalized Commuting Probability Of Finite Group"},"content":{"rendered":"\t\t
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Edumania-An International Multidisciplinary Journal<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Vol-02, Issue-04 (Oct -Dec 2024)<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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An International scholarly\/ academic journal, peer-reviewed\/ refereed journal, ISSN : 2960-0006<\/h5>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Studying The Computational Approaches And Algorithms For Calculating The Generalized Commuting Probability Of Finite Group<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Gunjan<\/span><\/p>

Research Scholar, Department of Mathematics, NIILM University Kaithal (Haryana)<\/span><\/p>

Jakhar, Manjeet Singh<\/span><\/p>

Associate Professor, Department of Mathematics, NIILM University, Kaithal (Haryana)<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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DOI:\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9091<\/span><\/a><\/p>

Page Number:\u00a0pp. 322-328<\/span><\/p>

Subject:\u00a0Group Theory, Abstract Algebra, Computational Mathematics, Finite Groups, Probability in Groups, Mathematical Algorithms<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Received:\u00a009 August 2024<\/span><\/p>

Accepted:\u00a006 September 2024<\/span><\/p>

Published:\u00a001 October 2024<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Thematic Classification:\u00a0Physical Sciences: Mathematics; Computational Mathematics; Algebra<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Abstract<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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The calculation of the generalized commuting probability, which quantifies the likelihood of subsets of elements commuting within a finite group, is a fundamental problem in computational group theory. This abstract presents an overview of methods and algorithms developed for efficiently computing the generalized commuting probability of finite groups. The presented approaches contribute to the advancement of computational group theory, enabling researchers and practitioners to explore and understand the structure and properties of finite groups in various mathematical and scientific domains.<\/span><\/p>

Keywords:<\/span> Probability, Group, Elements, F<\/span>inite ring, Algorithms <\/span>\u00a0\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Impact Statement<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Commutativity degree and its extensions, the relative commutativity degree and the n-th commutativity degree, are investigated in this study our findings offer insight on the features and dynamics of finite groups and enhance our knowledge of the commutative behaviour of algebraic structures. In addition to cryptography and coding theory, this research may also provide light on the study of symmetry in mathematical\u00a0systems.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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About The Author<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Dr Manjeet Singh Jakhar<\/b> have a great work ethic and believe that a great attitude and hard work are the key characteristics for success at university and a future career as a math professor. He is self- disciplined, having problem solving capability to achieve a successful outcome. He is confident that his passion for the subject matter, diligence and enthusiasm will allow him to not only be a successful student but ultimately to pursue important results in pure mathematics which help in future research work.<\/span><\/span><\/span><\/p>

I have a great work ethic and believe that a great attitude and hard work are the key characteristics for success at university and a future career as a math professor. I am self- disciplined, having problem solving capability to achieve a successful outcome. I am confident that my passion for the subject matter, dilligence and enthusiasm will allow me to not only be a successful student but ultimately to pursue important results in pure mathematics Which help in future\u00a0research\u00a0work.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Cite this Article<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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APA (7th ed.):<\/span>\u00a0Gunjan, & Jakhar, M. S. (2024). Studying The Computational Approaches And Algorithms For Calculating The Generalized Commuting Probability Of Finite Group.\u00a0<\/span>Edumania-An International Multidisciplinary Journal<\/span>,\u00a02(4), 322\u2013328.\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9091<\/span><\/a><\/p>

Chicago (17th ed.):<\/span>\u00a0Gunjan, and Manjeet Singh Jakhar. “Studying The Computational Approaches And Algorithms For Calculating The Generalized Commuting Probability Of Finite Group.”\u00a0<\/span>Edumania-An International Multidisciplinary Journal<\/span>\u00a02, no. 4 (2024): 322\u2013328.\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9091<\/span><\/a>.<\/span><\/p>

MLA (9th ed.):<\/span>\u00a0Gunjan, and Manjeet Singh Jakhar. “Studying The Computational Approaches And Algorithms For Calculating The Generalized Commuting Probability Of Finite Group.”\u00a0<\/span>Edumania-An International Multidisciplinary Journal<\/span>, vol. 2, no. 4, 2024, pp. 322\u2013328.\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9091<\/span><\/a>.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Statements & Declarations<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Peer Review:<\/span>\u00a0The academic rigor and contribution of this computational mathematics research to group theory have been validated through a rigorous and independent peer-review process conducted by experts in the discipline.<\/span><\/p>

Review Type:<\/span>\u00a0This manuscript was reviewed under a double-blind peer review model. This process, administered by the editorial team, ensured that the identities of the authors (Gunjan and Manjeet Singh Jakhar) and the reviewers were kept confidential from one another. The review was conducted by subject experts in abstract algebra, group theory, and computational mathematics.<\/span><\/p>

Competing Interests:<\/span>\u00a0The authors, Gunjan and Manjeet Singh Jakhar, jointly and individually declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.<\/span><\/p>

Data Availability:<\/span>\u00a0All data generated or analyzed during this study, including the computational algorithms and numerical results, are fully included within this published article. No external datasets were required for the validation of this theoretical and computational work.<\/span><\/p>

Funding:<\/span>\u00a0This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. The work was completed as part of the authors’ research affiliation with NIILM University, Kaithal.<\/span><\/p>

License:<\/span>\u00a0This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) 4.0 International License. This license permits copying and redistribution of the material in any medium or format for non-commercial purposes only, provided the original work is properly cited, and it does not permit adaptation or remixing of the material.<\/span><\/p>

Ethical Approval:<\/span>\u00a0Ethical approval was not required for this study, as it is a theoretical and computational mathematics work and did not involve the collection of data from, or experimentation on, human subjects or animals. It adheres to the highest standards of academic integrity and research ethics in mathematical sciences.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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References<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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  1. Detomi, Eloisa & Shumyatsky, Pavel. (2021). On the commuting probability for subgroups of a finite group.<\/span><\/p><\/li>

  2. Sharma, Uday Bhaskar & Singh, Anupam. (2020). Commuting probability and simultaneous conjugacy classes of commuting tuples in a group.<\/span><\/p><\/li>

  3. Goldstein, Avraham & Cherniavsky, Yonah & Levit, Vadim & Shwartz, Robert. (2017). Hultman Numbers and Generalized Commuting Probability in Finite Groups. Journal of Integer Sequences. 20. Article 17.10.7.<\/span><\/p><\/li>

  4. Buckley, S. M. and Machale, D. Commuting probability for subrings and quotient rings. Journal of Algebra Combinatorics Discrete Structures and Applications, 4(2):189-196, 2017.<\/span><\/p><\/li>

  5. Dutta, Parama & Nath, Rajat. (2016). On commuting probability of finite rings II.<\/span><\/p><\/li>

  6. Dutta, Jutirekha & Basnet, Dhiren & Nath, Rajat. (2015). On commuting probability of finite rings. Indagationes Mathematicae. 28. 10.1016\/j.indag.2016.10.002.<\/span><\/p><\/li>

  7. M. Soule, A Single Family of Semigroups with Every Positive Rational Commuting Probability Probability. College Mathematics Journal, 45 (2) (2014), 136 – 139.<\/span><\/p><\/li>

  8. Peter Hegarty. Limit points in the range of the commuting probability function on finite groups. Journal of Group Theory, 16(2):235\u2013247, 2013.<\/span><\/p><\/li>

  9. Salemkar, Alireza & Tavallaee, Hamid & Mohammadzadeh, Hamid. (2010). A remark on the commuting probability in finite groups. Southeast Asian Bulletin of Mathematics. 34.<\/span><\/p><\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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    Edumania-An International Multidisciplinary Journal Vol-02, Issue-04 (Oct -Dec 2024) An International scholarly\/ academic journal, peer-reviewed\/ refereed journal, ISSN : 2960-0006 Studying The Computational Approaches And Algorithms For Calculating The Generalized Commuting Probability Of Finite Group Gunjan Research Scholar, Department of Mathematics, NIILM University Kaithal (Haryana) Jakhar, Manjeet Singh Associate Professor, Department of Mathematics, NIILM University, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9298,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-10071","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/10071","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/comments?post=10071"}],"version-history":[{"count":6,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/10071\/revisions"}],"predecessor-version":[{"id":29396,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/10071\/revisions\/29396"}],"up":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/9298"}],"wp:attachment":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/media?parent=10071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}