Prove that $G$ is an abelian group given the following automorphism of $G$
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
108425
Problem on abelian group
90811
If $[G' : G'']\leq p^2$, then $G'$ is abelian.
126513
Automorphism of the group of rational numbers under addition
46263
Automorphisms of infinite abelian groups
25439
f(a) = inverse of a is an isomorphism iff a group G is Abelian
74964
Showing Galois Group is Abelian
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
73571
Proof of Cauchy's Theorem for abelian groups
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
3462
Proving a set of automorphisms of a group is a group under composition
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
108310
$(a_1 a_2 \cdots a_n)^2=e$ in a finite abelian group
151699
Group of inner automorphisms of a group $G$
56650
Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic