Show that $\phi :G\to{\rm Sym}(X)$ is a homomorphism.
14531
How group action works.
91222
Isomorphism between $\mathfrak o(4,\mathbb R)$ and $\mathfrak o (3,\mathbb R) \oplus\mathfrak o (3,\mathbb R) $
151993
Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
52556
Isomorphism of $S^1$.
143451
Homomorphism from $(\Bbb Q,+)$ to a finite group
13717
Homomorphisms from $S_4$ to $\mathbb Z_2$
48291
Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
134858
Abelian Group Homomorphism
137011
showing $\psi: R\to \mathbb C$ is ring isomorphism.
13764
Homomorphisms from $\mathbb{Z} \rightarrow S_3$.
90616
When is mapping $g$ to $g^{-1}$ a group homomorphism?
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
44258
Conditions under which group solvability is invariant under an homomorphism.
1026
Ring homomorphism with $\phi(1_R) \neq1_S$
32443
Find the kernel of a ring homomorphism $f(x)\to f(\sqrt 2)$
6171
Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$