Permutation Group & Symmetric Group ($S_n$) | Group Theory | RPSC 1st Grade & CSIR NET Maths
Автор: Gurpath Classes
Загружено: 2025-12-20
Просмотров: 49
Master Permutation Groups and the Symmetric Group ($S_n$), a crucial topic in Abstract Algebra (Group Theory) for RPSC 1st Grade, 2nd Grade, and CSIR NET Mathematical Sciences.In this video, we break down complex concepts into simple, exam-oriented explanations with solved examples.
📌 Topics Covered in this Class:Introduction: Definition of Permutation and Symmetric Group ($S_n$).Cycle Notation: How to write permutations in disjoint cycles.
Order of an Element: Finding the order of permutations using LCM.Transpositions: Understanding 2-cycles.Even & Odd Permutations: Concept of Sign of Permutation.Alternating Group ($A_n$): Definition and Order ($n!/2$).
Important Theorems: Cayley’s Theorem (Basic idea) and properties of $S_3$ and $S_4$.Previous Year Questions (PYQs): Solved problems from RPSC and NET exams.
🎯 Useful for Exams:RPSC 1st Grade (School Lecturer) - MathematicsRPSC 2nd Grade (Senior Teacher) - MathematicsCSIR NET JRF (Mathematical Sciences)SET / GATE Mathematics
Assistant Professor Exams💡 Key Formulas:Order of Symmetric Group $|S_n| = n!$Order of Alternating Group $|A_n| = n! / 2$
!#GroupTheory #PermutationGroup #RPSC1stGrade #CSIRNETMaths #AbstractAlgebra
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