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In this lecture by IFAS, Chandan Sir explores core concepts of Group Theory and Linear Algebra with a focus on problem-solving for competitive exams. This session is a key part of the Target CUET PG Mathematics 2026 series, designed for aspirants to build a strong conceptual foundation and improve problem-solving skills for abstract structures and their applications. 🔥 Join India's Best Mathematics Coaching for IIT JAM and CUET PG Exams - IFAS Online! STARTING SOON: Champion 2.2 Batch (From 19 Feb 2026) 👉🏻 IFAS IIT JAM and CUET PG Mathematics Result👈🏻: 🌟 IIT JAM 2025 - Total Selections: 1000+ (IIT JAM AIR 1,3,4,6,7,8....) 🌟CUET PG 2025 - Total Selections: 1500+ 🌟IIT JAM 2024: Total Selections: 800+ (IIT JAM AIR 1, 2, 3, 4, 8, 10...) 🌟CUET PG 2024: Total Selections: 500+ 🌟IIT JAM 2023: Total Selections: 600+ (IIT JAM AIR 1, 2, 8, 9...) 🌟IIT JAM 2022: Total Selections: 500+ (IIT JAM AIR 1, 4, 7, 10...) ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 👇 Watch the Full Lecture to Master These Topics: Quotient Groups Group Homomorphisms On-to (Surjective) Homomorphisms Injective Homomorphisms Normal Subgroups Center of a Group Cyclic and Abelian Properties ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ ⏱️ Timestamps - Jump to Your Topic: [00:36] Problem 1: Properties of Quotient Groups for $|G|=36$ [06:08] Problem 2: Determining Kernel Order for Homomorphisms (30 to 20 Order Groups) [12:50] Problem 3: Group Homomorphisms from $\mathbb{Z}_{12}$ to $\mathbb{Z}_{18}$ [14:05] Problem 4: Counting Surjective Homomorphisms [16:52] Problem 5: Non-Trivial Homomorphisms from $\mathbb{Z}_{7}$ to Groups of Order 49 [21:52] Problem 6: Fundamental Theorem of Group Homomorphisms and Quotient Isomorphisms [27:03] Problem 7: Calculating Injective Homomorphisms from $\mathbb{Z}_{6}$ to $S_5$ [37:23] Problem 8: Normal Subgroups in Groups of Order 45 [41:15] Problem 9: Subgroups Contained in the Center and their Normality [48:16] Problem 10: Index $p$ Subgroups and the Smallest Prime Divisor Result ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ Lecture Summary: In this session, Chandan Sir focus on "Top 500 Questions" for Algebra, providing a bridge between conceptual definitions and competitive exam applications. The lecture covers everything from basic homomorphism counting to advanced theorems involving normal subgroups and group centers. Chandan Sir emphasizes the importance of the Smallest Prime Index Theorem and provides a roadmap for a complete Abstract Algebra Revision scheduled for the upcoming Sunday at 8:00 AM. The session concludes by highlighting the ₹1 Test Series available on the IFAS app to help students manage time and minimize errors before the CUET PG exam. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 🔗 Important Links: 🌍 Visit our Website: https://ifasonline.com/iit-jam/mathem... 📞 Contact for Queries: 9172266888 📲 WhatsApp: https://whatsapp.com/channel/0029VbCV... 📘 Get Detailed Free Counselling: https://ifasonline.com/iit-jam/mathem... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ Download IFAS: 👇 📲Android: https://play.google.com/store/apps/de... 📲 Ios: https://apps.apple.com/us/app/ifas/id... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ IIT JAM Mathematics Live & Recorded Course – https://ifasonline.com/iit-jam/mathem... CUET PG Mathematics Live & Recorded Course – https://ifasonline.com/cuet-pg/mathem... Buy IIT JAM Mathematics Books – https://ifasonline.com/cuet-pg/mathem... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 📞 Contact for Admission: 9172266888 Stay Updated Via Other Social Media: ✔Telegram Discussion Group: https://t.me/IITJAM_NBHM_MScEntranceM... ✔Instagram: / ifas_maths__iit_jam_cuet_nbhm ✔Facebook: / mscentrancemaths ✔WhatsApp: https://api.whatsapp.com/send?phone=9... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ #iitjam #iitjammathematics #iitjammaths #iitjammath #mathematics #cuetpgmathematics #cuetpg #ifas #tifr