Welcome to our YouTube tutorial on "Subgroups in Group Theory"! In this educational journey, we'll unravel the concept of subgroups—a fundamental aspect of abstract algebra and group theory. In this tutorial, you'll learn: The formal definition of a subgroup and how it relates to the parent group. The criteria that a subset must meet to qualify as a subgroup. Different types of subgroups and their applications. The concept of cyclic subgroups and their role in group theory. Real-world examples illustrating the importance of subgroups. The statement and formulation of Lagrange's Theorem. How Lagrange's Theorem relates to the orders of groups and their subgroups. Real-world applications and implications of Lagrange's Theorem. The role of Lagrange's Theorem in understanding cosets and factor groups. Practical examples to solidify your understanding of this powerful theorem. subgroup in group theory | closure properties of subgroup | subgroup in discrete mathematics | subgroup theorem |subgroup examples,lagrange's theorem | Subgroup | subgroup properties | subgroup of a group | GATE Mathematics | discrete mathematics | group theory | group theory discrete mathematics | subgroups abstract algebra Contact Details (You can follow me at) Instagram: https://www.instagram.com/ahmadshoebkhan/ LinkedIn: https://www.linkedin.com/in/ahmad-shoeb-957b6364/ Facebook: https://www.facebook.com/ahmadshoebkhan Watch Complete Playlists: Data Structures: https://www.youtube.com/watch?v=jEMmThJ-1ss Theory of Computation: https://www.youtube.com/watch?v=p1oqDS0fayc Compiler Design: https://www.youtube.com/watch?v=XMt-KL-xn7k Design and Analysis of Algorithms:    • Design and Analysis of Algorithms   Graph Theory: https://www.youtube.com/watch?v=KB00Ogt36nM #subgroup #grouptheory #closureproperties #discretestructure #discretemathematics #discrete_mathematics #subgrouptheorem #lagrange'stheorem #subgroupproperties