Simple homomorphism of groups question
125582
Let $\phi:G_1\to G_2$ be a group homomorphism. Show $\phi(g^{-1})=(\phi(g))^{-1}$.
134858
Abelian Group Homomorphism
130081
Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
106347
Why is the image of a homomorphism a subgroup of the codomain?
133664
When the automorphism group is trivial......
48818
Homomorphism of local rings
101064
Showing the triviality of homomorphisms
108691
Characterize the natural numbers $n$ such that there is a surjective group homomorphism from $S_n$ to $S_{n-1}$.
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
119648
For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
8066
Sort-of-simple non-Hopfian groups
48397
Index of a sublattice in a lattice and a homomorphism between them
90192
Kernel and Image of a group homomorphism
7938
Number of Homomorphisms from $\Bbb{Z}_m$ to $\Bbb{Z}_n$
58707
Prove Quotient Group Isomorphism
151193
Simple subgroup of Symmetric Group