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Let H be the quotient group  Consider the following statements.
I. Every cyclic subgroup of H is finite.
II. Every finite cyclic group is isomorphic to a subgroup of H.
Which one of the following holds?
  • a)
    I is true but II is false
  • b)
    II is true but I is false
  • c)
    both I and II are true
  • d)
    neither I nor II is true
Correct answer is option 'C'. Can you explain this answer?
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Let H be the quotient groupConsider the following statements.I. Every cyclic subgroup of H is finite.II. Every finite cyclic group is isomorphic to a subgroup of H.Which one of the following holds?a)I is true but II is falseb)II is true but I is falsec)both I and II are trued)neither I nor II is trueCorrect answer is option 'C'. Can you explain this answer?
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Let H be the quotient groupConsider the following statements.I. Every cyclic subgroup of H is finite.II. Every finite cyclic group is isomorphic to a subgroup of H.Which one of the following holds?a)I is true but II is falseb)II is true but I is falsec)both I and II are trued)neither I nor II is trueCorrect answer is option 'C'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let H be the quotient groupConsider the following statements.I. Every cyclic subgroup of H is finite.II. Every finite cyclic group is isomorphic to a subgroup of H.Which one of the following holds?a)I is true but II is falseb)II is true but I is falsec)both I and II are trued)neither I nor II is trueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let H be the quotient groupConsider the following statements.I. Every cyclic subgroup of H is finite.II. Every finite cyclic group is isomorphic to a subgroup of H.Which one of the following holds?a)I is true but II is falseb)II is true but I is falsec)both I and II are trued)neither I nor II is trueCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Let H be the quotient groupConsider the following statements.I. Every cyclic subgroup of H is finite.II. Every finite cyclic group is isomorphic to a subgroup of H.Which one of the following holds?a)I is true but II is falseb)II is true but I is falsec)both I and II are trued)neither I nor II is trueCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free.
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