showing the group is abelian
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
18415
Direct sum of Abelian groups and Isomorphism
74586
Prove that every group of order $4$ is abelian
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
108425
Problem on abelian group
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
31380
Exponent and abelian groups
80976
Direct Product Of Abelian Group
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
26624
Prove that is group is abelian
92430
Show that the group is cyclic.
13355
Product of elements of a finite abelian group
59007
Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
35913
Abelianization of free group is the free abelian group
1577
Order of nontrivial elements is 2 implies Abelian group