Let $G$ be a group with order $p$ a prime number. Show $G$ is cyclic.
13734
Show that every group of prime order is cyclic
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
132280
Let $G$ be a group of order 35. Show that $G \cong Z_{35}$
100605
let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in G$
54453
Finite abelian $p$-group with only one subgroup size $p$ is cyclic
47478
Show that any cyclic group of even order has exactly one element of order $2$
109053
Show that a finite cyclic group of order $n$ has exactly one subgroup of order $d$ dividing $n$ and these are all the subgroups it has
104460
When a group is cyclic
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
98145
If $G$ is cyclic then $G/H$ is cyclic?
99205
Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
152481
If order of group is $p^2$, where $p$ is prime, how can you deduce $G$ is isomorphic to $C_{p^2}$ or $C_p \times C_p$?
147517
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
138108
If a normal subgroup $N$ of order $p$($p$ prime) is contained in a group $G$ of order $p^n$,then $N$ is in the center of $G$.
89382
In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.