Mathematics Exam > Mathematics Questions > Let G be a group of order 17 , The total numb...
Start Learning for Free
Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)?
Most Upvoted Answer
Let G be a group of order 17 , The total number of non - isomorphic su...
Introduction:
To find the total number of non-isomorphic subgroups of a group of order 17, we need to consider the possible orders of the subgroups and use the fact that the order of a subgroup must divide the order of the group.
Explanation:
The order of a subgroup must divide the order of the group. Since the order of the group is 17, the possible orders of subgroups are 1, 17.
Case 1: Order 1:
There is only one subgroup of order 1, which is the trivial subgroup {e}, where e is the identity element of the group.
Case 2: Order 17:
There is only one subgroup of order 17, which is the group itself, G.
Conclusion:
Therefore, there are a total of 2 non-isomorphic subgroups of G, namely {e} and G itself. Hence, the answer is B.) 2.
Visually Appealing Answer:
- Introduction: To find the total number of non-isomorphic subgroups of a group of order 17, we need to consider the possible orders of the subgroups and use the fact that the order of a subgroup must divide the order of the group.
- Explanation: The order of a subgroup must divide the order of the group. Since the order of the group is 17, the possible orders of subgroups are 1, 17.
- Case 1: Order 1: There is only one subgroup of order 1, which is the trivial subgroup {e}, where e is the identity element of the group.
- Case 2: Order 17: There is only one subgroup of order 17, which is the group itself, G.
- Conclusion: Therefore, there are a total of 2 non-isomorphic subgroups of G, namely {e} and G itself. Hence, the answer is B.) 2.
To find the total number of non-isomorphic subgroups of a group of order 17, we need to consider the possible orders of the subgroups and use the fact that the order of a subgroup must divide the order of the group.
Explanation:
The order of a subgroup must divide the order of the group. Since the order of the group is 17, the possible orders of subgroups are 1, 17.
Case 1: Order 1:
There is only one subgroup of order 1, which is the trivial subgroup {e}, where e is the identity element of the group.
Case 2: Order 17:
There is only one subgroup of order 17, which is the group itself, G.
Conclusion:
Therefore, there are a total of 2 non-isomorphic subgroups of G, namely {e} and G itself. Hence, the answer is B.) 2.
Visually Appealing Answer:
- Introduction: To find the total number of non-isomorphic subgroups of a group of order 17, we need to consider the possible orders of the subgroups and use the fact that the order of a subgroup must divide the order of the group.
- Explanation: The order of a subgroup must divide the order of the group. Since the order of the group is 17, the possible orders of subgroups are 1, 17.
- Case 1: Order 1: There is only one subgroup of order 1, which is the trivial subgroup {e}, where e is the identity element of the group.
- Case 2: Order 17: There is only one subgroup of order 17, which is the group itself, G.
- Conclusion: Therefore, there are a total of 2 non-isomorphic subgroups of G, namely {e} and G itself. Hence, the answer is B.) 2.
Community Answer
Let G be a group of order 17 , The total number of non - isomorphic su...
Answer is option B
because the total no of non isomorphic subgroup is tao(17) which is equal to 2
because the total no of non isomorphic subgroup is tao(17) which is equal to 2
|
Explore Courses for Mathematics exam
|
|
Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)?
Question Description
Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)?.
Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)?.
Solutions for Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)? defined & explained in the simplest way possible. Besides giving the explanation of
Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)?, a detailed solution for Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)? has been provided alongside types of Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)? theory, EduRev gives you an
ample number of questions to practice Let G be a group of order 17 , The total number of non - isomorphic subgroup of G is _____ A.) 1 B.) 2 C.) 3 D.) 17 (With explaine)? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© 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