Let $a,b,c \in G$ and $G$ is a group, prove that the following items have the same order...
34973
Is it true that the order of $ab$ is always equal to the order of $ba$?
79055
Orders of a symmetric group
30676
$G'$ and the product of all the elements in an odd order group
83710
Order of a homomorphism of groups
26398
Group of even order contains an element of order 2
124309
$g\in G$ maximal order in $G$ abelian then $G=\left\oplus H$
59811
Finite Abelian groups with the same number of elements for all orders are isomorphic
121423
Prove that every element of a finite group has an order
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
132127
Proving a direct product of groups is a group
15210
Group of order 6 proof
5042
Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.
80273
Prove the centralizer of an element in group $G$ is a subgroup of $G$
88440
Is G a CLT group if its order is product of distinct prime?
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
145406
Prove every element of $G$ has finite order.
83654
Order of an element in a finite cyclic group