Let p be a prime. If range(f) has an element of order p, then G has an element of order p.
123419
Abstract algebra: homomorphism and an element of a prime order
53475
Let $H$ have order $m$ and $K$ have order $n$, where $m$ and $n$ are relatively prime. Then $H \cap K=\{e\}$
65511
Proving the following false: $f(x)=2x+1$ produces a prime number if and only if x is prime
55429
Why does a Galois field have to have an order of $p^n$ where $p$ is prime?
19668
Does every group whose order is a power of a prime p contain an element of order p?
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
146572
Prove that between any two roots of $f$ there exists at least one root of $g$
56234
Isomorphism $f$ preserves the order of an element?
135586
Prove that the preimage of a prime ideal is also prime.
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
84789
Order of products of elements in a finite Abelian group
121423
Prove that every element of a finite group has an order
86626
Finite fields, existence of field of order $p^n$,proof help
61550
Existence of elements of order $p^k$ in a finite group
152481
If order of group is $p^2$, where $p$ is prime, how can you deduce $G$ is isomorphic to $C_{p^2}$ or $C_p \times C_p$?
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 $D_p$