Normal Subgroup | Cosets, Theorems & Klein Four Group Examples | B.Sc. 1st Year Maths скачать в хорошем качестве

Normal Subgroup | Cosets, Theorems & Klein Four Group Examples | B.Sc. 1st Year Maths

Normal Subgroup | Cosets, Theorems & Klein Four Group Examples | B.Sc. 1st Year Maths Welcome to K.Mathematics In this video, we study one of the most important topics of Group Theory — Normal Subgroups, designed strictly according to the B.Sc. 1st Year syllabus of Introduction to Algebra and Number Theory. This lecture covers cosets, definition of normal subgroup, important theorems, normal subgroup tests, and solved problems, including detailed examples from the Klein Four Group (K₄). The explanation is step-by-step, exam-oriented, and conceptually clear, making it ideal for college students and competitive exam aspirants. ⏱️ Time Stamps (Chapter-wise Explanation) 🕒 0:00 – Introduction 🕒 0:28 – Cosets: Definition of left and right cosets with explanation and examples. 🕒 3:24 – Normal Subgroup: Definition of normal subgroup, notation, and conceptual meaning. 🕒 5:24 – Theorem -1 & Theorem -2(Equivalent conditions for normal subgroups and Normal Subgroup Test.) 🕒 8:58 – Theorem -3 Every subgroup of an abelian group is normal (with proof). 🕒 10:32 – Theorem -5(A subgroup is normal if the product of two right cosets is again a right coset.) 🕒 12:58 – Problem 1 (Klein Four Group) Normal subgroups of the Klein Four Group 🕒 15:31 – Problem 2 (Another solved problem related to normal subgroups.) 🕒 17:38 – Problem 3 (Proof that the center of a group is a normal subgroup.) 🕒 18:48 – Outro 🎯 What You Will Learn in This Video ✔ Definition of cosets ✔ Left coset vs right coset ✔ Definition of normal subgroup ✔ Normal subgroup tests ✔ Important theorems with proofs ✔ Solved problems on Klein Four Group ✔ Center of a group as a normal subgroup ✔ Exam-oriented explanations 🎓 Who Should Watch This Video? B.Sc. 1st Year Mathematics students Students studying Introduction to Algebra & Number Theory CSIR-NET / GATE / JAM aspirants Anyone learning Group Theory from basics 📌 Syllabus Covered B.Sc. Mathematics – Paper: Introduction to Algebra and Number Theory Unit: Group Theory (Cosets & Normal Subgroups) 👍 Support the Channel If you find this video helpful: 🔔 Subscribe to K.Mathematics 👍 Like | 💬 Comment | 🔁 Share with classmates Your support helps in creating quality mathematics content for students. Your Queries: normal subgroup cosets in group theory left coset right coset normal subgroup test group theory bsc 1st year introduction to algebra and number theory klein four group k4 group abelian group normal subgroup center of a group quotient group basics factor group group theory examples group theory theorems abstract algebra bsc normal subgroup proof coset examples group theory lecture group theory full chapter bsc mathematics group theory college algebra mathematics algebra for beginners normal subgroup explained cosets and normal subgroups maths honours bsc bsc 1st year maths syllabus group theory problem solving group theory tutorial group theory exam preparation csir net group theory basics iit jam algebra basics gate mathematics group theory klein four group examples k mathematics channel abstract algebra lecture subgroup normality group homomorphism basics normal subgroup definition maths for undergraduate indian university mathematics group theory notes algebra concepts algebra one shot group theory beginners bsc 1st year maths right cosets in klein’s four group cosets in group theory examples examples of cosets in group theory normal subgroups of the group of quaternions cosets and Lagrange’s theorem examples klein four group which are the normal subgroups of the group of quaternions properties of normal subgroup bsc 1st year normal subgroup properties of cosets in group theory normal subgroups cosets of a subgroup finding cosets of a subgroup cosets in group theory #NormalSubgroup #Cosets #GroupTheory #KleinFourGroup #K4Group #AbstractAlgebra #BScMathematics #BSc1stYear #CollegeMaths #Algebra #IntroductionToAlgebra #AlgebraAndNumberTheory #GroupTheoryLecture #GroupTheoryBasics #NormalSubgroupTest #CosetsInGroupTheory #AbelianGroup #CenterOfGroup #QuotientGroup #FactorGroup #MathsForBSc #MathsHonours #CSIRNETMaths #IITJAMMaths #GATEMath seematics #UndergraduateMaths #MathsLecture #MathsConcepts #UniversityMaths #IndianUniversityMaths #KMATHEMATICS #KMathematics #GroupTheoryProblems #AlgebraLecture #MathsEducation #MathsTutorial #LearnAlgebra #kmathematics #education #bscmathematics #conicsections #maths #engineering #fmuniversity #analyticgeometry #nep2025 #kishan #utkaluniversity #nep2020 #nep