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(i) Every subgroup of a cyclic group is also cyclic.
(ii) Every proper subgroup of an infinite cyclic group is infinite.
  • a)
    (i) & (ii) True
  • b)
    (i) True & (ii) False
  • c)
    (i) False & (ii) True
  • d)
    (i) & (ii) False
Correct answer is option 'A'. Can you explain this answer?
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(i) Every subgroup of a cyclic group is also cyclic.(ii) Every proper ...
A non empty subset H of a group G is said to be a subgroup of G. If under the operation defined on G. H itself forms a group. According to result on sub-group
(i) Every subgroup of a cyclic group is also cyclic.
(ii) Every proper subgroup of an infinite cyclic group is infinite.
Both are true.
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(i) Every subgroup of a cyclic group is also cyclic.(ii) Every proper ...
A non empty subset H of a group G is said to be a subgroup of G. If under the operation defined on G. H itself forms a group. According to result on sub-group
(i) Every subgroup of a cyclic group is also cyclic.
(ii) Every proper subgroup of an infinite cyclic group is infinite.
Both are true.
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Community Answer
(i) Every subgroup of a cyclic group is also cyclic.(ii) Every proper ...
These are both theorems
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(i) Every subgroup of a cyclic group is also cyclic.(ii) Every proper subgroup of an infinite cyclic group is infinite.a)(i) & (ii) Trueb)(i) True & (ii) Falsec)(i) False & (ii) Trued)(i) & (ii) FalseCorrect answer is option 'A'. Can you explain this answer?
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