Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > One-Step Subgroup Test
One-Step Subgroup Test Video Lecture | Mathematics for Competitive Exams
|
98 videos|27 docs|30 tests
|
FAQs on One-Step Subgroup Test Video Lecture - Mathematics for Competitive Exams
| 1. What is the One-Step Subgroup Test? |  |
Ans. The One-Step Subgroup Test is a method used in mathematics to determine if a subset of a group is a subgroup. It involves checking if the subset is closed under the group operation, contains the identity element, and contains the inverse of each of its elements.
| 2. How is the One-Step Subgroup Test applied in mathematics? | |
Ans. To apply the One-Step Subgroup Test, we need to check three conditions: closure, identity, and inverses. Firstly, we need to verify that the subset is closed under the group operation, meaning that if we combine any two elements from the subset, their result must also be in the subset. Secondly, the subset must contain the identity element of the group. Finally, for every element in the subset, its inverse must also be in the subset.
| 3. Can you provide an example of applying the One-Step Subgroup Test? | |
Ans. Sure! Let's consider the group of integers under addition, denoted as (Z, +). If we want to determine if the subset {0, 2, 4, 6} is a subgroup, we can apply the One-Step Subgroup Test. Firstly, we check closure: adding any two elements from the subset gives us another element in the subset. Secondly, the identity element of (Z, +) is 0, which is also in the subset. Lastly, for every element in the subset, its inverse is also in the subset. Therefore, {0, 2, 4, 6} satisfies all the conditions and is a subgroup of (Z, +).
| 4. What happens if a subset fails the One-Step Subgroup Test? | |
Ans. If a subset fails the One-Step Subgroup Test, it means that it is not a subgroup of the given group. This indicates that the subset lacks one or more of the required properties, such as closure, identity, or inverses. In such cases, the subset cannot be considered a subgroup.
| 5. Are there any alternative methods to determine if a subset is a subgroup? | |
Ans. Yes, there are alternative methods to determine if a subset is a subgroup. One common method is the Two-Step Subgroup Test, which involves verifying closure and inverses separately. Another approach is to use the Subgroup Criterion, which states that a non-empty subset of a group is a subgroup if and only if it is closed under the group operation and contains the inverse of each of its elements. Both of these methods can be used as alternatives to the One-Step Subgroup Test.
Related Exams
About this Video
|
Dec 23, 2024 Last updated |
Video Description: One-Step Subgroup Test for Mathematics 2024 is part of Mathematics for Competitive Exams preparation.
The notes and questions for One-Step Subgroup Test have been prepared according to the Mathematics exam syllabus.
Information about One-Step Subgroup Test covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for One-Step Subgroup Test.
Introduction of One-Step Subgroup Test in English is available as part of our Mathematics for Competitive Exams for Mathematics & One-Step Subgroup Test 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 One-Step Subgroup Test Video Lecture | Mathematics for Competitive Exams - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for Competitive Exams.
Information about One-Step Subgroup Test
Here you can find the meaning of One-Step Subgroup Test defined & explained in the simplest way possible.
Besides explaining types of One-Step Subgroup Test theory, EduRev gives you an ample number of questions to practice One-Step Subgroup Test 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
Exam
,Important questions
,Objective type Questions
,Previous Year Questions with Solutions
,MCQs
,past year papers
,ppt
,One-Step Subgroup Test Video Lecture | Mathematics for Competitive Exams
,practice quizzes
,Sample Paper
,Semester Notes
,shortcuts and tricks
,One-Step Subgroup Test Video Lecture | Mathematics for Competitive Exams
,Extra Questions
,study material
,Summary
,Free
,video lectures
,mock tests for examination
,Viva Questions
,One-Step Subgroup Test Video Lecture | Mathematics for Competitive Exams
;
Study One-Step Subgroup Test on the App
Students of Mathematics can study One-Step Subgroup Test alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the One-Step Subgroup Test,
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 One-Step Subgroup Test 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