Show a homomorphic image on a group is a subgroup
106347
Why is the image of a homomorphism a subgroup of the codomain?
113413
How do I show that two groups are not isomorphic?
143451
Homomorphism from $(\Bbb Q,+)$ to a finite group
58076
Subgroup generated by a set
124237
Group equals union of three subgroups
24181
Showing that $G$ is a group under an alternative operation.
27728
Question on a homomorphism of a set G.
44258
Conditions under which group solvability is invariant under an homomorphism.
98474
Show the existence of a certain subgroup of F2
63780
to show characteristic subgroup is normal in G
76962
Sylow $p$-subgroups of $GL_n(\mathbb{F}_p)$
106809
$f: G→G$ defined by $f(x) =x^2$ is a homomorphism if and only if $G$ is abelian.
1220
Have $\alpha:G \to H$. If a subgroup $U$ is normal in $H$ prove the pre-image of $U$ is normal in $G$.
98739
If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then $$|G:K|=|G:H||H:K|$$
134858
Abelian Group Homomorphism
121257
Image of Homomorphism of Lie groups
44165
the image of normal subgroups