All the $m$th powers commute with each other and all the $n$th powers commute with each other, $m$ and $n$ relative prime, is abelian.
26148
A group such that $a^m b^m = b^m a^m$ and $a^n b^n = b^n a^n$ ($m$, $n$ coprime) is abelian?
47623
The set of all complex homomorphisms of abelian group $G$ has the same structure as $G$
40287
Prove: if $a,b\in G$ commute with probability $>5/8$, then $G$ is abelian
70861
$\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$
143069
What are the direct summands in $\mathbb{Z}^n$?
19352
Normal subgroup of index m contains every element of order n where m and n are relatively prime
141258
Why does $M \mathbin{\otimes_R} N \cong M_\mathfrak{p} \mathbin{\otimes_{R_\mathfrak{p}}} N$?
140199
Proof that disjoint cycles commute
134820
$p$ prime, Group of order $p^n$ is cyclic iff it is an abelian group having a unique subgroup of order $p$
24966
Converse of Lagrange's theorem for abelian groups
14528
Proof that all abelian simple groups are cyclic groups of prime order
26661
Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
18018
Proving that $4 \mid m - n$ is an equivalence relation on $\mathbb{Z}$
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
46342
Prove that $G$ is abelian iff $\varphi(g) = g^2$ is a homomorphism
97800
Exterior power "commutes" with direct sum
49977
Show that the collection of matrices which commute with every idempotent matrix are the scalar matrices