Suppose $G$ is a group of order 11. Then every non-identity element is a generator of $G$
13734
Show that every group of prime order is cyclic
114187
In a finite cyclic group, the generator has the order of the group
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$
41688
An elementary problem in Group Theory: the unique noncyclic group of order 4
1577
Order of nontrivial elements is 2 implies Abelian group
18881
Number of elements of order $7$ in a group
96123
Element of maximal order in alternating group $A_{10}$: how to prove this is it?
92057
Prove that for every odd integer n, there is a group...
44729
Prove $g$ is a generator if $g^q=1 \pmod p$
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
128899
How to find all generators for a cyclic group of order $n$?
51145
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
79995
G is group of order pq, pq are primes
24181
Showing that $G$ is a group under an alternative operation.
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$