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Q.19 consider the group (, +) and its subgroup (z, +). for the quoticnt group q/2, which onc of the following is false? (a) 2/2 contains a subgroup isomorphic t
Q.19 Consider the group (, +) and its subgroup (Z, +). For the quoticnt group Q/2, which onc of the following is FALSE? (A) 2/2 contains a subgroup isomorphic to (2, +). (B) There is exactly one group homomorphism from Q/Z to (Q +). (C) For all EN, there exists g E Q/Z such that the order of g is n. (D) Q/7 is not a cyclic group.
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Navdeep goyal 1 Best Answer
Q/Z={Z+p/q ;p/q€Q} let q(Z+p/q)=Z+q.p/q=Z+p=Z(zero of Q/Z) so order of each element of Q/Z is finite let H is subgroup of Q/Z then H is not isomorphic to Z bcz order of each element of H is finite but order of each element of Z is not finite. so options A