How prove a group is not free abelian group
2719
Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
118022
Show that a group of order $180$ is not simple.
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
151287
Isomorphic abelian groups which are not isomorphic R-modules
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
82485
Show that the set of non zero rationals is not a cyclic group under multiplication.
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
11003
Proving that $G/N$ is an abelian group
51359
Prove that every subgroup of an abelian group is a normal subgroup.
48393
Abelian groups of order n.
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$