the group homomorphism $f:G\rightarrow H$ is exactly then an injection when $ker(f)=eG$
34234
Kernel of injective group homomorphism
142698
Proving that the fundamental groups of two spaces with same homotopy type are isomorphic
38691
Injectivity of Homomorphism in Localization
151993
Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
17997
Right identity and Right inverse implies a group
18540
Isomorphism from $\mathbb{C}[G]$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.
136083
Show that $\sigma\circ\phi : G_1 \to G_3$ is an isomorphism
144988
Commutator Subgroup of Direct Product equals the Direct Product of the Commutator Subgroups
33455
Question on group homomorphisms involving the standard Z-basis
158282
Finite order of an element $f(g)$ of a homomorphism $f$
129162
Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
62454
Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.
61593
Adjoint map is Lie homomorphism
57732
Rings of fractions and homomorphisms
114221
A Group $G$ is soluble $\iff G^{(k)}=\{e\}$ for some $k$
27670
Group homomorphisms $\mathbb{Q}\to\mathbb{R}$