{"id":10079,"date":"2024-12-02T06:45:45","date_gmt":"2024-12-02T06:45:45","guid":{"rendered":"https:\/\/icertpublication.com\/?page_id=10079"},"modified":"2026-03-07T07:23:02","modified_gmt":"2026-03-07T01:53:02","slug":"investigating-algebraic-simple-groups-with-conjugacy-classes-and-products","status":"publish","type":"page","link":"https:\/\/icert.org.in\/index.php\/edu-mania\/edumania-vol-02-issue-04\/investigating-algebraic-simple-groups-with-conjugacy-classes-and-products\/","title":{"rendered":"Investigating Algebraic Simple Groups With Conjugacy Classes And Products"},"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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Investigating Algebraic Simple Groups With Conjugacy Classes And Products<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Anju<\/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\/9092<\/span><\/a><\/p>

Page Number:\u00a0pp. 329-335<\/span><\/p>

Subject:\u00a0Group Theory, Abstract Algebra, Finite Simple Groups, Conjugacy Classes, Algebraic Structures, Pure Mathematics<\/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; Algebra; Group Theory<\/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\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Algebraic simple groups, being non-abelian and lacking proper normal subgroups, represent a profound and captivating domain within group theory and algebraic geometry. In the pursuit of understanding these enigmatic entities, the study of conjugacy classes and products emerges as a key to unlocking their underlying symmetries and structures. Group members can be partitioned into different sets with the use of conjugacy classes, which group together equivalent elements under inner automorphisms to show similar algebraic features. The analysis of conjugacy classes provides deep insights into the dynamics and character of algebraic simple groups. On the other hand, group products explore the interactions between distinct elements, generating new elements within the group and unraveling its internal symmetries.<\/span><\/p>

Keywords<\/span>:<\/span>Conjugacy,Algebraic, Groups, Products,Semisimple<\/span><\/i><\/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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Member of the same conjugacy class cannot be distinguished by using only the group structure, and therefore share many properties. The study of conjugacy classes of non-Abelian group is fundamental for the study of their structure for an abelian group, each conjugacy class is a set containing\u00a0one\u00a0element (Singleton Set).<\/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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My particular pleasure is pure mathematics. I have found mathematics a fascinating subject since my early years.\u00a0 I enjoy it as it is challenging and logical. I look forward to university life and facing both the academic and social challenges head-on. I am confident that my passion for the subject matter, diligence and enthusiasm will allows me to not only be a successful Student, but ultimately to pursue a successful Career in business upon these foundations.<\/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>\u00a0Anju, & Jakhar, M. S. (2024). Investigating Algebraic Simple Groups With Conjugacy Classes And Products.\u00a0<\/span>Edumania-An International Multidisciplinary Journal<\/span>,\u00a02(4), 329\u2013335.\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9092<\/span><\/a><\/p>

Chicago (17th ed.):<\/span>\u00a0Anju, and Manjeet Singh Jakhar. “Investigating Algebraic Simple Groups With Conjugacy Classes And Products.”\u00a0<\/span>Edumania-An International Multidisciplinary Journal<\/span>\u00a02, no. 4 (2024): 329\u2013335.\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9092<\/span><\/a>.<\/span><\/p>

MLA (9th ed.):<\/span>\u00a0Anju, and Manjeet Singh Jakhar. “Investigating Algebraic Simple Groups With Conjugacy Classes And Products.”\u00a0<\/span>Edumania-An International Multidisciplinary Journal<\/span>, vol. 2, no. 4, 2024, pp. 329\u2013335.\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9092<\/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 scholarly quality and contribution of this research on algebraic simple groups have been confirmed through a rigorous and independent peer-review process conducted by experts in the relevant fields.<\/span><\/p>

Review Type:<\/span>\u00a0This article underwent a double-blind peer review, wherein the identities of the authors (Anju and Manjeet Singh Jakhar) and the reviewers were concealed from each other. The review was conducted by subject experts in abstract algebra, group theory, and pure mathematics.<\/span><\/p>

Competing Interests:<\/span>\u00a0The authors, Anju 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 mathematical proofs and theoretical derivations, are fully included within this published article. This is a theoretical mathematics paper and does not rely on external datasets.<\/span><\/p>

Funding:<\/span>\u00a0The authors received no specific financial support, grants, or funding from any public, commercial, or not-for-profit organization for the research, authorship, and\/or publication of this article. 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 allows others to download this work and share it with others for non-commercial purposes, as long as they credit the authors, but they cannot change it in any way or use it commercially.<\/span><\/p>

Ethical Approval:<\/span>\u00a0Ethical approval was not required for this study, as it is a theoretical mathematics work and did not involve the collection of data from, or experimentation on, human subjects or animals. The work adheres to the highest standards of academic integrity and research ethics in mathematical sciences.<\/span><\/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. Simion, Iulian. (2022). Products of conjugacy classes in simple algebraic groups in terms of diagrams. Communications in Algebra. 51. 1-15. 10.1080\/00927872.2022.2159034.<\/span><\/p><\/li>

  2. Ahanjideh, Neda. (2019). A note on the product of conjugacy classes of a finite group. Monatsheftef\u00fcrMathematik. 190. 10.1007\/s00605-019-01273-x.<\/span><\/p><\/li>

  3. Simion, Iulian. (2019). Sheets of conjugacy classes in simple algebraic groups. MATHEMATICA. 61 (84). 183-189. 10.24193\/mathcluj.2019.2.08.<\/span><\/p><\/li>

  4. Beltr\u00e1n, Antonio & Felipe, Mar\u00eda&Melchor, Carmen. (2019). New Progress in Products of Conjugacy Classes in Finite Groups. 10.1017\/9781108692397.007.<\/span><\/p><\/li>

  5. Guralnick, Robert &Moret\u00f3, Alexander. (2018). Conjugacy classes, characters and products of elements.<\/span><\/p><\/li>

  6. Guralnick, Robert &Malle, Gunter. (2013). Products of commutators and classes in algebraic groups. MathematischeAnnalen. 362. 10.1007\/s00208-014-1128-1.<\/span><\/p><\/li>

  7. Guralnick, Robert &Malle, Gunter &Tiep, Pham. (2012). Products of conjugacy classes in finite and algebraic simple groups. Advances in Mathematics. 234. 10.1016\/j.aim.2012.11.005.<\/span><\/p><\/li>

  8. Moori, Jamshid& Tong-Viet, Hung. (2011). Products of conjugacy classes in simple groups. QuaestionesMathematicae. 34. 433-439. 10.2989\/16073606.2011.640452.<\/span><\/p><\/li>

  9. Guralnick, Robert &Malle, Gunter. (2010). Products of conjugacy classes and fixed point spaces. Journal of the American Mathematical Society. 25. 10.2307\/23072152.<\/span><\/p><\/li><\/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 Investigating Algebraic Simple Groups With Conjugacy Classes And Products Anju Research Scholar, Department of Mathematics, NIILM University, Kaithal (Haryana) Jakhar, Manjeet Singh Associate Professor, Department of Mathematics, NIILM University, Kaithal (Haryana) DOI:\u00a0https:\/\/doi.org\/10.59231\/edumania\/9092 Page Number:\u00a0pp. 329-335 […]<\/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-10079","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/10079","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=10079"}],"version-history":[{"count":9,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/10079\/revisions"}],"predecessor-version":[{"id":29405,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/10079\/revisions\/29405"}],"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=10079"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}