$G=\{e,a,b,c\}$, $|G|=4$, non-cyclic, then what are the orders of the elements?
41688
An elementary problem in Group Theory: the unique noncyclic group of order 4
145127
For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
50762
If $S_n$ has cyclic subgroups of these orders or not?
79055
Orders of a symmetric group
33216
Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.
140673
how to find the order of an element in a quotient group
147517
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
106653
How many generator has a cyclic group of order n?
107010
How many elements of order $k$ are in $S_n$?
56607
gcd and order of elements of group
79380
How to find the order of a group generated by two elements?
96123
Element of maximal order in alternating group $A_{10}$: how to prove this is it?
45156
Every group of order $35$ is cyclic?
5089
An element of a group has the same order as its inverse
53357
Cyclic Group Generators of Order $n$
33300
Showing order of $Z (G) =1$ or $pq$
62035
Order of automorphism group of cyclic group