{"id":10071,"date":"2024-12-02T06:35:02","date_gmt":"2024-12-02T06:35:02","guid":{"rendered":"https:\/\/icertpublication.com\/?page_id=10071"},"modified":"2024-12-03T05:13:50","modified_gmt":"2024-12-03T05:13:50","slug":"studying-the-computational-approaches-and-algorithms-for-calculating-the-generalized-commuting-probability-of-finite-group","status":"publish","type":"page","link":"https:\/\/icertpublication.com\/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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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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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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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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    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, Kaithal (Haryana) Abstract The calculation of the generalized commuting probability, which quantifies the likelihood of subsets of elements commuting within […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9298,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"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"],"_links":{"self":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/10071","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/comments?post=10071"}],"version-history":[{"count":10,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/10071\/revisions"}],"predecessor-version":[{"id":10090,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/10071\/revisions\/10090"}],"up":[{"embeddable":true,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/9298"}],"wp:attachment":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/media?parent=10071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}