Group Theory | One Short Series | CSIR NET July 2026 | Lec- 1 | IFAS

Group Theory | One Shot Series | CSIR NET July 2026 | Lec-1 | IFAS explained with clear concepts and exam‑focused approach. Master group structure, subgroup counting, normal subgroups, Sylow theorems, and homomorphisms with PYQs, tricks, and smart problem‑solving for CSIR NET and other competitive exams.

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⏳ Lecture Timeline:
[00:00:00] – Introduction of Group Theory
[00:03:43] – Group Theory Quick Revision
[00:04:14] – Segment: Group Structure
[00:07:29] – Question 1: Group of Order 8
[00:12:04] – Question 2: Finite p‑Group Ep(G)
[00:14:24] – Important: Order Divides n
[00:17:37] – Question 3: Primitive Root Mod 29 (PYQ)
[00:30:00] – Question 4: Divisible Groups
[00:40:45] – Question 5: Proper Subgroup Union (S3)
[00:43:50] – Question 6: Order 8 True Statements
[00:50:21] – Question 7: GP Set & Characteristic Subgroup
[01:04:06] – Important: Characteristic ⇒ Normal
[01:08:35] – Question 8: Group as Subgroup Union
[01:16:41] – Question 9: Primitive Roots Mod p (PYQ)
[01:19:40] – Formula: a^k Primitive Condition
[01:21:42] – Question 10: Element Orders in S7
[01:24:55] – Question 11: Normal Subgroups of S4
[01:28:04] – Question 12: Non‑Abelian of Order pq
[01:32:28] – Question 13: Simple Group Property A
[01:37:05] – Question 14: Homomorphisms D4 to C4
[01:43:42] – Question 15: Exactly Three Subgroups
[01:49:50] – Question 16: Homomorphism & Order
[01:56:00] – Question 17: Automorphism Groups
[02:02:04] – Question 18: Normal Subgroup Intersection
[02:06:56] – Important: Normality Not Transitive
[02:10:32] – Question 19: Quotient Cyclic/Abelian
[02:19:36] – Question 20: Finite p‑Group Properties
[02:22:21] – Important: p‑Group Center Non‑Trivial
[02:24:58] – Question 21: Group of Order 45
[02:27:30] – Question 22: Group of Order 385 (PYQ)
[02:31:29] – Sylow: 11‑SSG Unique & Normal
[02:38:30] – Question 23: Group of Order 30
[02:48:22] – Question 24: Group of Order 36 (Not Simple)
[02:55:32] – Question 25: Sylow 7‑Subgroup Normalizer
[02:56:50] – Formula: |G|/|N(P)| = # Sylow p‑Subgroups
[02:58:36] – Complete Session (Group Theory )
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📖 Topics Covered in This Lecture:
• Group Structure: Element Orders, Isomorphic Groups & Properties
• Proper Subgroups & Union of Subgroups PYQ
• Normal Subgroups, Quotient Groups & Homomorphisms
• Sylow Theorems: Counting, Normality & Subgroup Index Tricks
• Automorphism Group & Characteristic Subgroups Concepts
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📚 Lecture Summary:
In this session, IFAS Expert Faculty focuses on Group Theory fundamentals including element orders, isomorphic groups (S3, Q8, D4, etc.), proper subgroups, union of subgroups, and Sylow theorems. Covers normal subgroups, homomorphisms, automorphism groups, and characteristic subgroups with PYQ-based problem‑solving. Strong emphasis on group theory tricks and exam‑relevant concepts ensures thorough revision for CSIR NET.
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🎓 This lecture is highly beneficial for students preparing for:
✅ CSIR NET Mathematical Science ✅ GATE Mathematics ✅ SET Mathematics
✅ TIFR Mathematics ✅ PhD Entrance Exams

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✅ CSIR NET Dec 2025: 4000+ Selections (AIR 3, 8, 9.....)
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✅ CSIR NET June 2024: 2000+ Selections (AIR 3, 10, 13...)
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