$G$ be a free abelian group of rank $k$ , let $S$ be a subset of $G$ that generates $G$ then is it true that $|S| \ge k$?
22629
rank of the free group: $\mathrm{rank} F_X=|X|$
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
68672
Commutator subgroup of rank-2 free group is not finitely generated.
82037
Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
68128
Two term free resolution of an abelian group.
51145
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
71420
Prove that a group is abelian.
5741
Direct product of abelian groups
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
148285
Generator of group $D_n$
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
98155
Free products of cyclic groups