Prove that an abelian group is not finitely generated.
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
17510
Proving a set is an abelian group.
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
82485
Show that the set of non zero rationals is not a cyclic group under multiplication.
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
133770
Subgroups of finite abelian groups.
43783
Abelian group (Commutative group)
81354
The product of all the elements of a finite abelian group
68971
Elementary approach to proving that a group of order 9 is Abelian
35913
Abelianization of free group is the free abelian group
152630
showing that a group of order 45 is abelian
13355
Product of elements of a finite abelian group
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
1577
Order of nontrivial elements is 2 implies Abelian group
105180
When does $(ab)^n = a^n b^n$ imply a group is abelian?