Prove that if $G$ is a cyclic group of order $n$, then $G$ is isomorphic to $\mathbb{Z}_{n}$.
61513
Prove that all cyclic groups of the same order are isomorphic
62035
Order of automorphism group of cyclic group
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
107716
Show that $G$ is cyclic
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
36887
Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
108213
$N_1,N_2,N_3 \unlhd G, N_i\cap N_j =\{e\}, G = N_iN_j$. Want to show that $G$ is abelian, $N_i$ are isomorphic.
59533
If $\gcd(m,n)=1$, then $\mathbb{Z}_n \times \mathbb{Z}_m$ is cyclic.
150007
Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group.
39938
Subgroups of a cyclic group and their order.
127603
If $G$ be a group of order $8$ and $x$ be a element of order $4$. Prove that $x^2 \in Z(G)$
28362
Product of two cyclic groups is cyclic iff their orders are co-prime
141890
$G$ is a Group of order $pq$, if $G$ has exactly one subgroup of order $p$ and another with order $q$, then $G$ is cyclic ($p,q$ are prime)
84823
When is the group of units in $\mathbb{Z}_n$ cyclic?
70904
Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups