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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)?
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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
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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)?
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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)?.
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