In a group of order $m p^n$ for $p$ prime, if $k<n$, is there an element of order $p^k$?
61550
Existence of elements of order $p^k$ in a finite group
99205
Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
152604
For a finite group of order $2n$ does there exist $x$ such that $x\ast x=e$?
134676
Number of elements of order $p$ is a multiple of $p-1$ (finite group).
104513
Order of elements in $Z_n$
101735
A finite $p$-group cannot be simple unless it has order $p$
53475
Let $H$ have order $m$ and $K$ have order $n$, where $m$ and $n$ are relatively prime. Then $H \cap K=\{e\}$
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
28676
Is a finite group uniquely determined by the orders of its elements?
19352
Normal subgroup of index m contains every element of order n where m and n are relatively prime
103423
Normal subgroup where G has order prime
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?
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
3703
Order of finite fields is $p^n$
55429
Why does a Galois field have to have an order of $p^n$ where $p$ is prime?
108309
An example of a non-abelian group of order $p^3$
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime