Speaker: Prof. Dr. Nor Haniza Sarmin – Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia (UTM)
Topic: Lagrange’s Theorem
Date: 25 March 2026
The Algebra Research Group had the honor of hosting a guest lecture by Prof. Dr. Nor Haniza Sarmin, specially designed for undergraduate students, introducing the fundamental concepts leading to Lagrange’s Theorem in group theory.
In her lecture, she began with the concept of cosets, 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.
She then introduced the notion of a subgroup and proceeded to define the index of a subgroup, 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.
Building on these concepts, she presented Lagrange’s Theorem, 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.
Throughout the lecture, she provided numerous examples to illustrate each concept, making the progression from cosets to Lagrange’s Theorem clear and accessible.
Overall, the lecture offered a well-structured and intuitive introduction to Lagrange’s Theorem, highlighting its foundational role in understanding the structure of finite groups.