Simple method the show that a group of order 15 is cyclic
6030
Group of order 15 is abelian
58397
Every cyclic group with order > 2 has at least 2 distinct generators
28362
Product of two cyclic groups is cyclic iff their orders are co-prime
117178
Cyclic group generators
70034
Showing that this set of functions is a group.
134455
Any group of order $15$ is abelian(without sylow theorem)
156319
Show that a group with $|G| = 33$ contains an element of order $3$
39938
Subgroups of a cyclic group and their order.
85106
Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
84501
Proof involving Cyclic group, generator and GCD
38687
Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$
102429
There are 2 groups of order 6 (up to isomorphism)
107716
Show that $G$ is cyclic
151025
If G is a group of order n=35, then it is cyclic
61394
The product of finitely many cyclic groups is cyclic
82878
Order of cyclic groups and the Euler phi function
148774
show elements of order 15 in $S_8$ satisfy a relation