Prove that a group $G$ is abelian
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
6153
Suppose that $G$ is a group with the property that for every choice of elements in $G$, $axb=cxd$ implies $ab=cd$. Prove that $G$ is Abelian.
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
51359
Prove that every subgroup of an abelian group is a normal subgroup.
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
156429
If $G$ is a group whereby $(a\cdot b)^{i} =a^i\cdot b^i$ for three consecutive integers $i$ for all $a, b \in G$, show $G$ is abelian.
57421
If $\forall x \in G$ where G is a group $x=x^{-1}$ then how is this group abelian?
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
90811
If $[G' : G'']\leq p^2$, then $G'$ is abelian.
107716
Show that $G$ is cyclic
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
43783
Abelian group (Commutative group)
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
24181
Showing that $G$ is a group under an alternative operation.
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
37971
Prove that the center of a group is a normal subgroup
150585
Group with $a=a^{-1}$ for all $a\in G$ is abelian