If G be a cyclic group of prime order p ,prove that non identity element of G is a generator of the group.
38853
Cyclic group of prime order
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group
145112
Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.
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)
80273
Prove the centralizer of an element in group $G$ is a subgroup of $G$
76504
Non-trivial cyclic group with unique generator
13734
Show that every group of prime order is cyclic
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
103423
Normal subgroup where G has order prime
117468
$o(g^{k})=\frac{o(g)}{\gcd(o(g),k)}$ order of a power of a group element.
53207
Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
61550
Existence of elements of order $p^k$ in a finite group