Why is the image of a homomorphism a subgroup of the codomain?
6466
Image of subgroup and Kernel of homomorphism form subgroups
61334
Application of Main Homomorphism Theorem
40678
Image of an ideal under a surjective ring homomorphism is an ideal
98474
Show the existence of a certain subgroup of F2
126930
Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
158282
Finite order of an element $f(g)$ of a homomorphism $f$
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
44258
Conditions under which group solvability is invariant under an homomorphism.
55900
Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
91956
Intuition of the meaning of homology groups
84114
Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
34234
Kernel of injective group homomorphism
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
117897
A homomorphism induces a continuous map from ${\rm Spec}(A') \to {\rm Spec}(A)$.
145339
Index of the subgroup $\operatorname{Im}(f)$
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
13764
Homomorphisms from $\mathbb{Z} \rightarrow S_3$.