Which one of the following is True?
  • a)
    Zn is cyclic if and only if n is prime.
  • b)
    Every proper subgroup of Zn is cyclic.
  • c)
    Every proper subgroup of S4 is cyclic.
  • d)
    If every proper subgroup of a group is cyclic, then the group is cyclic.
Correct answer is option 'B'. Can you explain this answer?

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This discussion on Which one of the following is True?a)Zn is cyclic if and only if n is prime.b)Every proper subgroup of Zn is cyclic.c)Every proper subgroup of S4 is cyclic.d)If every proper subgroup of a group is cyclic, then the group is cyclic.Correct answer is option 'B'. Can you explain this answer? is done on EduRev Study Group by IIT JAM Students. The Questions and Answers of Which one of the following is True?a)Zn is cyclic if and only if n is prime.b)Every proper subgroup of Zn is cyclic.c)Every proper subgroup of S4 is cyclic.d)If every proper subgroup of a group is cyclic, then the group is cyclic.Correct answer is option 'B'. Can you explain this answer? are solved by group of students and teacher of IIT JAM, which is also the largest student community of IIT JAM. If the answer is not available please wait for a while and a community member will probably answer this soon. You can study other questions, MCQs, videos and tests for IIT JAM on EduRev and even discuss your questions like Which one of the following is True?a)Zn is cyclic if and only if n is prime.b)Every proper subgroup of Zn is cyclic.c)Every proper subgroup of S4 is cyclic.d)If every proper subgroup of a group is cyclic, then the group is cyclic.Correct answer is option 'B'. Can you explain this answer? over here on EduRev! Apart from being the largest IIT JAM community, EduRev has the largest solved Question bank for IIT JAM.
This discussion on Which one of the following is True?a)Zn is cyclic if and only if n is prime.b)Every proper subgroup of Zn is cyclic.c)Every proper subgroup of S4 is cyclic.d)If every proper subgroup of a group is cyclic, then the group is cyclic.Correct answer is option 'B'. Can you explain this answer? is done on EduRev Study Group by IIT JAM Students. The Questions and Answers of Which one of the following is True?a)Zn is cyclic if and only if n is prime.b)Every proper subgroup of Zn is cyclic.c)Every proper subgroup of S4 is cyclic.d)If every proper subgroup of a group is cyclic, then the group is cyclic.Correct answer is option 'B'. Can you explain this answer? are solved by group of students and teacher of IIT JAM, which is also the largest student community of IIT JAM. If the answer is not available please wait for a while and a community member will probably answer this soon. You can study other questions, MCQs, videos and tests for IIT JAM on EduRev and even discuss your questions like Which one of the following is True?a)Zn is cyclic if and only if n is prime.b)Every proper subgroup of Zn is cyclic.c)Every proper subgroup of S4 is cyclic.d)If every proper subgroup of a group is cyclic, then the group is cyclic.Correct answer is option 'B'. Can you explain this answer? over here on EduRev! Apart from being the largest IIT JAM community, EduRev has the largest solved Question bank for IIT JAM.