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Group Theory: Permutation Group Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
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FAQs on Group Theory: Permutation Group Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is a permutation group? |  |
Ans. A permutation group is a mathematical concept that represents a set of permutations (rearrangements) of a given set. It is a group because it follows the group axioms: closure, associativity, identity, and inverse.
| 2. How do permutation groups relate to symmetry? | |
Ans. Permutation groups are closely related to symmetry because they describe all possible ways to rearrange the elements of a set while preserving its structure. In other words, permutation groups capture the symmetries of an object or a system.
| 3. Can you give an example of a permutation group? | |
Ans. Sure! Consider the set {1, 2, 3}. The permutation group of this set consists of all possible ways to rearrange these three elements. For example, one permutation could be (1, 2, 3), another could be (2, 1, 3), and so on. All these permutations form a permutation group.
| 4. What are the key properties of a permutation group? | |
Ans. The key properties of a permutation group include closure (the composition of any two permutations in the group is also in the group), associativity (permutation composition is associative), identity (there exists an identity permutation), and inverse (for every permutation, there exists an inverse permutation).
| 5. How are permutation groups used in mathematics and other fields? | |
Ans. Permutation groups have numerous applications in various fields. In mathematics, they are used to study symmetry in abstract algebra, group theory, and combinatorics. In computer science, permutation groups are employed in algorithms for solving problems related to permutations and symmetries. They also find applications in physics, chemistry, and cryptography, among other areas.
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