Prove that $G$ is isomorphic to $\text{Inn}(G)$ if $G$ has trivial center $Z(G)$.
32362
Detail in bijection between Inn(G) and G/Z(G)?
72251
$g\circ f$ is Surjective and $g$ is Injective then Prove that $f$ is surjective
43759
Prove that the set $\mathrm{Aut}(G)$ of all automorphisms of the group $G$ with the operation of taking the composition is a group
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
151047
a non trivial example: $G/H$ is isomorphic to $G$
78553
A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$
146969
Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
148881
Aut(GxH) isomorphic to Aut(G)xAut(H)
62455
Prove Equivalence Relation in G
70912
If $g\circ f$ is injective and $f$ is surjective then $g$ is injective
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
37971
Prove that the center of a group is a normal subgroup
87766
Using Cayley's Theorem to find an isomorphic subgroup.
94090
How to show that for any abelian group $G$, $\text{Hom}(\mathbb{Z},G)$ is isomorphic to $G$
59041
Centre of $GL_n(\mathbb R)$
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .