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Order of an Element in Group Theory Video Lecture | Mathematics for Competitive Exams
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FAQs on Order of an Element in Group Theory Video Lecture - Mathematics for Competitive Exams
| 1. What is the order of an element in group theory? |  |
Ans. The order of an element in group theory refers to the smallest positive integer n such that raising the element to the power of n results in the identity element of the group.
| 2. How is the order of an element calculated in group theory? | |
Ans. To calculate the order of an element in group theory, one can systematically raise the element to different powers until the identity element is obtained. The smallest power required to achieve this is the order of the element.
| 3. Can the order of an element be infinite in group theory? | |
Ans. No, in group theory, the order of an element cannot be infinite. Every element in a group must have a finite order, meaning there exists a positive integer n such that raising the element to the power of n gives the identity element.
| 4. What is the significance of the order of an element in group theory? | |
Ans. The order of an element in group theory provides important information about the structure of the group. It helps determine the possible subgroups and can be used to classify groups into different categories based on the orders of their elements.
| 5. Can the order of an element in a group be greater than the order of the group itself? | |
Ans. No, the order of an element in a group cannot be greater than the order of the group itself. By Lagrange's theorem in group theory, the order of any subgroup must divide the order of the group. Therefore, the order of an element, which represents the order of the cyclic subgroup it generates, cannot exceed the order of the group.
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Nov 22, 2024 Last updated |
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