if $𝐺$ is a finite abelian group $𝑜(𝑎)$ divides the exponent of $𝐺$, for each $𝑎\in 𝐺$
7079
ord $(b)|\max\{\text{ord}(g)|g\in G\}$ for all $b\in G\,$ a finite abelian group
83654
Order of an element in a finite cyclic 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.
112872
Involutions and Abelian Groups
138862
Product of all elements in an odd finite abelian group is 1
121077
Product of all elements in finite group
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
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 $x^2=e$.
122125
Order of group element divides order of finite group
3203
Quotient group $\mathbb Z^n/\ \text{im}(A)$
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
74586
Prove that every group of order $4$ is abelian
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
68733
If $G/Z(G)$ is cyclic then $G$ is abelian – what is the point?
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
113936
Showing that a finite abelian group has a subgroup of order m for each divisor m of n
150585
Group with $a=a^{-1}$ for all $a\in G$ is abelian