Mathematics Exam > Mathematics Videos > Algebra > Concept of Subgroup
Concept of Subgroup Video Lecture | Algebra - Mathematics
|
161 videos|58 docs
|
FAQs on Concept of Subgroup Video Lecture - Algebra - Mathematics
| 1. What is a subgroup? |  |
Ans. A subgroup is a subset of a group that maintains the same algebraic structure as the larger group. It is closed under the group operation, contains the identity element of the group, and contains the inverse of each of its elements.
| 2. How is a subgroup different from a group? | |
Ans. While a group is a complete set with a specific algebraic structure, a subgroup is a subset of a group that shares the same algebraic structure. A subgroup inherits its properties from the larger group, but it may have fewer elements and restrictions compared to the group itself.
| 3. Can a subgroup have more elements than the original group? | |
Ans. No, a subgroup cannot have more elements than the original group. By definition, a subgroup is a subset of a group, which means it contains fewer or an equal number of elements as the group itself.
| 4. How can we determine if a subset is a subgroup of a given group? | |
Ans. To determine if a subset is a subgroup of a given group, we need to check three conditions: closure, identity element, and inverses. The subset must be closed under the group operation, contain the identity element of the group, and contain the inverse of each of its elements.
| 5. Can a subgroup have multiple identity elements? | |
Ans. No, a subgroup cannot have multiple identity elements. The identity element is unique within a group, and a subgroup must contain the same identity element as the larger group. Therefore, a subgroup can only have one identity element.
Related Exams
About this Video
|
4.77/5 Rating |
|
Nov 09, 2024 Last updated |
Video Description: Concept of Subgroup for Mathematics 2024 is part of Algebra preparation.
The notes and questions for Concept of Subgroup have been prepared according to the Mathematics exam syllabus.
Information about Concept of Subgroup covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Concept of Subgroup.
Introduction of Concept of Subgroup in English is available as part of our Algebra for Mathematics & Concept of Subgroup in
Hindi for Algebra 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 Concept of Subgroup Video Lecture | Algebra - Mathematics - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Algebra.
Information about Concept of Subgroup
Here you can find the meaning of Concept of Subgroup defined & explained in the simplest way possible.
Besides explaining types of Concept of Subgroup theory, EduRev gives you an ample number of questions to practice Concept of Subgroup tests,
examples and also practice Mathematics tests.
|
161 videos|58 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
Free
,Important questions
,Previous Year Questions with Solutions
,Extra Questions
,Concept of Subgroup Video Lecture | Algebra - Mathematics
,Concept of Subgroup Video Lecture | Algebra - Mathematics
,Concept of Subgroup Video Lecture | Algebra - Mathematics
,Sample Paper
,past year papers
,study material
,Objective type Questions
,MCQs
,Viva Questions
,Semester Notes
,video lectures
,Exam
,Summary
,shortcuts and tricks
,ppt
,practice quizzes
,mock tests for examination
;
Study Concept of Subgroup on the App
Students of Mathematics can study Concept of Subgroup alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Concept of Subgroup,
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 Concept of Subgroup is prepared as per the latest Mathematics syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup