Mathematics Exam > Mathematics Questions > Which of the following is not true?a)The orde...
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Which of the following is not true?
- a)The order of the subgroup of a finite group divides the order of the group
- b)Every group of infinite order is cyclic
- c)Every cyclic group is abelian
- d)If k is a divisor of the order of a group G, then G must have a subsrouo of order k
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Which of the following is not true?a)The order of the subgroup of a fi...
α = (1 3) (2 5 4)
|order of (1 3) = 2
order of (2 5 4) = 3
order of α = 1.c.m. of 2 and 3 = 6
|order of (1 3) = 2
order of (2 5 4) = 3
order of α = 1.c.m. of 2 and 3 = 6
Most Upvoted Answer
Which of the following is not true?a)The order of the subgroup of a fi...
Explanation:
Statement d: If k is a divisor of the order of a group G, then G must have a subgroup of order k
- This statement is not true. It is possible for a group to have a divisor of its order that does not correspond to a subgroup of that order.
- For example, consider the group of integers under addition. The order of this group is infinite. However, it does not have a subgroup of order 2, even though 2 is a divisor of infinity.
- Therefore, it is not always the case that if k is a divisor of the order of a group G, then G must have a subgroup of order k.
Statement d: If k is a divisor of the order of a group G, then G must have a subgroup of order k
- This statement is not true. It is possible for a group to have a divisor of its order that does not correspond to a subgroup of that order.
- For example, consider the group of integers under addition. The order of this group is infinite. However, it does not have a subgroup of order 2, even though 2 is a divisor of infinity.
- Therefore, it is not always the case that if k is a divisor of the order of a group G, then G must have a subgroup of order k.
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Community Answer
Which of the following is not true?a)The order of the subgroup of a fi...
α = (1 3) (2 5 4)
|order of (1 3) = 2
order of (2 5 4) = 3
order of α = 1.c.m. of 2 and 3 = 6
|order of (1 3) = 2
order of (2 5 4) = 3
order of α = 1.c.m. of 2 and 3 = 6
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Which of the following is not true?a)The order of the subgroup of a finite group divides the order of the groupb)Every group of infinite order is cyclicc)Every cyclic group is abeliand)If k is a divisor of the order of a group G, then G must have a subsrouo of order kCorrect answer is option 'D'. Can you explain this answer?
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Which of the following is not true?a)The order of the subgroup of a finite group divides the order of the groupb)Every group of infinite order is cyclicc)Every cyclic group is abeliand)If k is a divisor of the order of a group G, then G must have a subsrouo of order kCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which of the following is not true?a)The order of the subgroup of a finite group divides the order of the groupb)Every group of infinite order is cyclicc)Every cyclic group is abeliand)If k is a divisor of the order of a group G, then G must have a subsrouo of order kCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is not true?a)The order of the subgroup of a finite group divides the order of the groupb)Every group of infinite order is cyclicc)Every cyclic group is abeliand)If k is a divisor of the order of a group G, then G must have a subsrouo of order kCorrect answer is option 'D'. Can you explain this answer?.
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