Showing a group is abelian
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
143550
Order of product of two elements in an abelian group
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group
108425
Problem on abelian group
108310
$(a_1 a_2 \cdots a_n)^2=e$ in a finite abelian group
81354
The product of all the elements of a finite abelian group
70034
Showing that this set of functions is a group.
66510
A group is abelian if and only if the center of the group is all the group
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.
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
74964
Showing Galois Group 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.
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?
5297
If G is a finite abelian group and $a_1,...,a_n$ are all its elements, show that $x=a_1a_2a_3...a_n$must satisfy $x^2=e$.
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
145159
Finite group is abelian if the representatives of its conjugacy classes commute