False proof? If $f: G \rightarrow H$ homomorphism, and $H$ abelian, then $G$ abelian?
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
11003
Proving that $G/N$ is an abelian group
149750
Help understanding Fundamental Theorem of Finite Abelian Groups
68728
Why does the natural ring homomorphism induce a surjective group homomorphism of units?
98542
Prove that $H$ is a subgroup of an abelian group $G$
133660
When can a homomorphism be determined entirely by its generators
27436
Does $G\cong G/H$ imply that $H$ is trivial?
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
144065
Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
40069
The image of a homomorphism is a group?
33455
Question on group homomorphisms involving the standard Z-basis
62454
Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.
140962
Counterexamples for $G \times H$ isomorphic to $G$ implies $H$ trivial.
129162
Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
75315
How to prove that homomorphism from field to ring is injective or zero?
100149
If there are injective homomorphisms between two groups in both directions, are they isomorphic?
158282
Finite order of an element $f(g)$ of a homomorphism $f$