Group homomorphism from finite abelian group to $\mathbb{C}\setminus\{0\}$
47623
The set of all complex homomorphisms of abelian group $G$ has the same structure as $G$
59811
Finite Abelian groups with the same number of elements for all orders are isomorphic
81354
The product of all the elements of a finite abelian group
3907
Abelian quotient group
3203
Quotient group $\mathbb Z^n/\ \text{im}(A)$
54911
The preimage of a normal subgroup under a group homomorphism is normal
78913
In a finite field, is there ever a homomorphism from the additive group to the multiplicative group?
34234
Kernel of injective group homomorphism
2153
How to get a homomorphism from $\mathbb{Z}\to G$, for $G$ a non-trivial group?
101064
Showing the triviality of homomorphisms
36882
Two finite abelian groups with the same number of elements of any order are isomorphic
106347
Why is the image of a homomorphism a subgroup of the codomain?
61334
Application of Main Homomorphism Theorem
97009
Image of ring homomorphism $\phi : \mathbb{Z}[t] \to \mathbb{Q}$?
94090
How to show that for any abelian group $G$, $\text{Hom}(\mathbb{Z},G)$ is isomorphic to $G$
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?