If $f$ is an automorphism and $|\{a: f(a) = a^{-1}\}| = 3/4 |G|$ then $G$ has an abelian subgroup of index $2$
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
57434
$SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3)) \cong A_4$
31380
Exponent and abelian groups
113936
Showing that a finite abelian group has a subgroup of order m for each divisor m of n
34606
Which groups have precisely two automorphisms
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
36965
Automorphism of rational numbers
155669
$\mathrm{Aut}(D_4)$ is isomorphic to $D_4$
106809
$f: G→G$ defined by $f(x) =x^2$ is a homomorphism if and only if $G$ is abelian.
145809
Automorphism group of a lie algebra as a lie subgroup of $GL(\frak g)$
158282
Finite order of an element $f(g)$ of a homomorphism $f$
49666
Generalization of index 2 subgroups are normal
109596
Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$
58654
If $|A| > \frac{|G|}{2} $ then $AA = G $
130745
Action of finite group of automorphisms on Spec A
3462
Proving a set of automorphisms of a group is a group under composition