For any $r$, $s$, $t>1$, then there's a group such that $x$ has order $r$, $y$ has order $s$ while $xy$ has order $t$?
114662
Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
150156
Proving that $S_n$ has order $n!$
10602
Monotone Union of subgroups being subgroup
102429
There are 2 groups of order 6 (up to isomorphism)
54195
Do groups of prime order have one subgroup?
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
124224
How many groups of order $n$ with center {e} exist?
113357
Groups of order $pqr$ and their normal subgroups
13807
Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S
25155
Suppose $R$ and $S$ are transitive relations on $A$. Prove that if $S \circ R \subseteq R \circ S$ then $R \circ S$ is transitive.
4402
Group of order $pqr$, $p < q < r$ primes
148904
Groups of order $p^3$
70001
Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)
152838
Relation between Ramsey Numbers: $R(s, t) > (t-1)(s-1)$
85579
$G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal