a and b commutes of order p q with p and q co-prime show that ab is order pq
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
123419
Abstract algebra: homomorphism and an element of a prime order
122970
A question on $p$-groups, and order of its commutator subgroup.
158355
If $A$ commutes with $B$ and $B$ commutes with $C$, then $A$ commutes with $C$
48607
If $A$ is normal and $A$ and $B$ commute, then $A^*$ and $B$ commute
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
50665
If $a,b$ is an $R$-sequence, then $ax-b$ is prime (Eisenbud, Exercise 10.4)
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
13734
Show that every group of prime order is cyclic
119758
On the order of elements of $\mathrm{GL}(2,q)$.
56097
If $A$ and $AB-BA$ commute, show that $AB-BA$ is nilpotent
74460
Matrices A+B=AB implies A commutes with B
103147
$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime
125030
Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.