Existence of an element of order $p$
73571
Proof of Cauchy's Theorem for abelian groups
39170
Existence of square root
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
124380
existence of sequence of polynomial
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
86626
Finite fields, existence of field of order $p^n$,proof help
38419
Existence of Polynomial with whom product contains only prime powers
101735
A finite $p$-group cannot be simple unless it has order $p$
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
100061
The Maximum possible order for an element $S_n$
120951
If a partial order has just one unique maximal element, must that element be a greatest element of x?
126569
Can we find a well ordering on an infinite set with no largest element?
15526
Question on groups of order $pq$
121423
Prove that every element of a finite group has an order
155190
Stone-Weierstrass theorem with $p(1/x)$