Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Algebra Group & Subgroups
Consider the group (Q, +) and its subgroup (Z, +).
For the quotient group Q/Z, which one of the following is FALSE?
1
Q/Z contains a subgroup isomorphic to (Z, +).
2
There is exactly one group homomorphism from Q/Z to (Q, +).
3
For all n ∈ N, there exists g ∈ Q/Z such that the order of g is n.
4
Q/Z is not a cyclic group.