{"id":580,"date":"2026-03-26T19:45:36","date_gmt":"2026-03-26T12:45:36","guid":{"rendered":"https:\/\/algebra.math-ugm.id\/?p=580"},"modified":"2026-03-26T19:47:24","modified_gmt":"2026-03-26T12:47:24","slug":"guest-lecture-an-introduction-to-algebraic-structure","status":"publish","type":"post","link":"https:\/\/algebra.math-ugm.id\/en\/guest-lecture-an-introduction-to-algebraic-structure\/","title":{"rendered":"Guest Lecture: An Introduction to Algebraic Structure"},"content":{"rendered":"

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Speaker:<\/strong> Prof. Dr. Nor Haniza Sarmin \u2013 Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia (UTM)
Topic:<\/strong> Lagrange\u2019s Theorem \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/em><\/p>\n

Date:\u00a0<\/strong>25 March 2026<\/p>\n

The Algebra Research Group had the honor of hosting a guest lecture by Prof. Dr. Nor Haniza Sarmin, specially designed for undergraduate students<\/strong>, introducing the fundamental concepts leading to Lagrange\u2019s Theorem<\/strong> in group theory.<\/p>\n

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In her lecture, she began with the concept of cosets<\/strong>, explaining how a group can be partitioned into left and right cosets of a subgroup. She illustrated these ideas with several concrete examples, helping participants build an intuitive understanding of how cosets behave within a group.\"\"<\/p>\n

She then introduced the notion of a subgroup<\/strong> and proceeded to define the index of a subgroup<\/strong>, emphasizing its meaning as the number of distinct cosets. Through examples, she demonstrated how to compute the index and how it reflects the structure of the group.\"\"<\/p>\n

Building on these concepts, she presented Lagrange\u2019s Theorem<\/strong>, showing that the order of a subgroup divides the order of the group. The result was explained clearly through the partition of the group into disjoint cosets, linking directly to the definition of index.\"\"<\/p>\n

Throughout the lecture, she provided numerous examples to illustrate each concept, making the progression from cosets to Lagrange\u2019s Theorem clear and accessible.<\/p>\n

Overall, the lecture offered a well-structured and intuitive introduction to Lagrange\u2019s Theorem, highlighting its foundational role in understanding the structure of finite groups.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

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Speaker: Prof. Dr. Nor Haniza Sarmin \u2013 Department of Mathematics, […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-580","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/580","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/comments?post=580"}],"version-history":[{"count":2,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/580\/revisions"}],"predecessor-version":[{"id":588,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/580\/revisions\/588"}],"wp:attachment":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/media?parent=580"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/categories?post=580"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/tags?post=580"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}