In Lecture 12 (Part 2) of the Group Theory series, Dubey Sir explores the Symmetry and Permutation on a Set. This lecture breaks down key concepts, provides step-by-step explanations, and showcases real-world applications in mathematics and cryptography. Whether you're preparing for CSIR NET, IIT JAM, or GATE, or just strengthening your algebraic foundation, this video is a must-watch!
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𝗟𝗲𝗰𝘁𝘂𝗿𝗲: 12 (Part 02)
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📚 Topics Covered:
1. Symmetry on a Set
2. Permutation on a Set
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This video is about;
What is the symmetric of a set?
What is a permutation on a set?
What is permutation symmetry?
How many symmetric relations are on a set?
What are symmetry examples?
How do you know if a set is symmetric or not?
What is permutation with example?
What is a permutation of a set of objects?
Symmetry, reflexivity and transitivity in set relations
What is a permutation of a set
symmetry of a set
Bidirectional Relationship
Order Matters
Reflexive vs. Symmetric
Symmetric relation
Symmetric relation example
Equivalence Relations
Symmetry on a set example
Symmetry on a set formula
Symmetric relation in Group Theory
Group
Subgroup
quotient group
Subset of a group
Index of a subgroup
One-Step Subgroup Test
Two-Step Subgroup Test
Finite subgroup Test
Subgroup Test Examples
One-step subgroup test example
Subgroup generated by a set
Subgroup generated by a subset
Subgroup generated by an element, for example
Normal subgroup generated by an element
order of a group and order of an element
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