Are all transpositions of a finite set conjugate to each other under action by inner automorphisms?
13771
Why are two permutations conjugate iff they have the same cycle structure?
13761
Automorphisms in $\mathbb{Z}_n$
121244
Homomorphisms and automorphisms on polynomial rings
69361
How do you find the automorphism?
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
146356
To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
73988
Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$
10350
Automorphisms of the complex plane
87830
Relating the union of the power set of a set to the set itself
99346
Prove a result on transitive group actions.
120968
Isomorphism of stabilizer over $S_n$ to $S_{n-1}$
3462
Proving a set of automorphisms of a group is a group under composition
97865
On Conjugacy Classes of Alternating Group $A_n$
148413
Proving $S_n$ is generated by the set $\{(1\text{ }2),(2\text{ }3),\cdots,(n-1\text{ }n)\}$ of $n-1$ transpositions.
103106
Proving that any permutation in $S_n$ can be written as a product of disjoint cycles
96025
Showing there is only one isomorphism between well ordered sets using transfinite induction
110018
Conjugacy classes in $A_n$.