Mathematics Exam > Mathematics Videos > Mathematics for IIT JAM, GATE, CSIR NET, UGC NET > Cyclic Group
Cyclic Group Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
|
556 videos|198 docs
|
FAQs on Cyclic Group Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is a cyclic group? |  |
A cyclic group is a mathematical structure consisting of a set of elements, along with an operation that combines any two elements to produce a third element. The group is said to be cyclic if there exists an element, called the generator, such that repeatedly applying the operation to the generator produces all the elements in the group.
| 2. How can we determine if a group is cyclic? | |
To determine if a group is cyclic, we need to check if there exists an element in the group that generates all other elements. This can be done by repeatedly applying the operation to a chosen element and checking if all elements are obtained. If such an element exists, the group is cyclic; otherwise, it is not.
| 3. What is the order of a cyclic group? | |
The order of a cyclic group is the number of elements it contains. In other words, it is the total count of distinct elements that can be generated by repeatedly applying the operation to the generator. The order is always a positive integer.
| 4. Can a cyclic group have more than one generator? | |
No, a cyclic group can have only one generator. This is because the generator must be able to produce all other elements in the group through repeated application of the operation. If there were multiple generators, one generator would not be able to generate all the elements produced by the other generators.
| 5. Are all cyclic groups finite? | |
No, not all cyclic groups are finite. While some cyclic groups have a finite number of elements, there are also cyclic groups that have an infinite number of elements. The order of a cyclic group can be finite (e.g., a cyclic group of integers modulo n) or infinite (e.g., a cyclic group of integers).
Related Exams
About this Video
|
4.96/5 Rating |
|
Dec 22, 2024 Last updated |
Video Description: Cyclic Group for Mathematics 2024 is part of Mathematics for IIT JAM, GATE, CSIR NET, UGC NET preparation.
The notes and questions for Cyclic Group have been prepared according to the Mathematics exam syllabus.
Information about Cyclic Group covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Cyclic Group.
Introduction of Cyclic Group in English is available as part of our Mathematics for IIT JAM, GATE, CSIR NET, UGC NET for Mathematics & Cyclic Group in
Hindi for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET 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 Cyclic Group Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET.
Information about Cyclic Group
Here you can find the meaning of Cyclic Group defined & explained in the simplest way possible.
Besides explaining types of Cyclic Group theory, EduRev gives you an ample number of questions to practice Cyclic Group tests,
examples and also practice Mathematics tests.
|
556 videos|198 docs
|
|
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
Summary
,Extra Questions
,ppt
,GATE
,Exam
,past year papers
,Cyclic Group Video Lecture | Mathematics for IIT JAM
,Free
,practice quizzes
,UGC NET
,UGC NET
,CSIR NET
,MCQs
,Important questions
,GATE
,shortcuts and tricks
,Previous Year Questions with Solutions
,Objective type Questions
,study material
,video lectures
,CSIR NET
,CSIR NET
,GATE
,Cyclic Group Video Lecture | Mathematics for IIT JAM
,mock tests for examination
,Semester Notes
,Sample Paper
,Cyclic Group Video Lecture | Mathematics for IIT JAM
,Viva Questions
,UGC NET
;
Study Cyclic Group on the App
Students of Mathematics can study Cyclic Group alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Cyclic Group,
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 Cyclic Group 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