Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Order of an Element in Group Theory
Order of an Element in Group Theory Video Lecture | Mathematics for Competitive Exams
|
98 videos|27 docs|30 tests
|
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.
Related Exams
About this Video
|
Dec 23, 2024 Last updated |
Video Description: Order of an Element in Group Theory for Mathematics 2024 is part of Mathematics for Competitive Exams preparation.
The notes and questions for Order of an Element in Group Theory have been prepared according to the Mathematics exam syllabus.
Information about Order of an Element in Group Theory covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Order of an Element in Group Theory.
Introduction of Order of an Element in Group Theory in English is available as part of our Mathematics for Competitive Exams for Mathematics & Order of an Element in Group Theory in
Hindi for Mathematics for Competitive Exams course. Download more important topics related with notes, lectures and mock test series for
Mathematics Exam by signing up for free.
Description
Video Lecture & Questions for Order of an Element in Group Theory Video Lecture | Mathematics for Competitive Exams - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for Competitive Exams.
Information about Order of an Element in Group Theory
Here you can find the meaning of Order of an Element in Group Theory defined & explained in the simplest way possible.
Besides explaining types of Order of an Element in Group Theory theory, EduRev gives you an ample number of questions to practice Order of an Element in Group Theory tests,
examples and also practice Mathematics tests.
|
98 videos|27 docs|30 tests
|
|
Explore Courses for Mathematics exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Sample Paper
,practice quizzes
,Semester Notes
,Order of an Element in Group Theory Video Lecture | Mathematics for Competitive Exams
,Summary
,mock tests for examination
,Free
,Objective type Questions
,video lectures
,Important questions
,Previous Year Questions with Solutions
,Order of an Element in Group Theory Video Lecture | Mathematics for Competitive Exams
,Viva Questions
,ppt
,study material
,shortcuts and tricks
,Order of an Element in Group Theory Video Lecture | Mathematics for Competitive Exams
,MCQs
,Exam
,past year papers
,Extra Questions
;
Study Order of an Element in Group Theory on the App
Students of Mathematics can study Order of an Element in Group Theory alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Order of an Element in Group Theory,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Order of an Element in Group Theory is prepared as per the latest Mathematics syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup