If a finite set $G$ is closed under an associative product and both cancellation laws hold, then it is a group
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
93666
Does the closedness of a subgroup $H$ of $G$ imply that for $h\in H, g\in G \setminus H : hg \not \in H$?
32253
How to prove $b=c$ if $ab=ac$ (cancellation law in groups)?
12459
Associativity of symmetric difference of sets
11957
G is the product of its Sylow subgroups
90584
Show set of affine transformations is a group
17510
Proving a set is an abelian group.
44258
Conditions under which group solvability is invariant under an homomorphism.
82843
Subgroups of $\Bbb{R}^n$ that are closed and discrete
141642
Closure of a certain subset in a compact topological group
152363
Cancellation in topological product
117701
Let $G$ be a group and $X$ set. $a,b \in X$ are in the same orbit, so show that $stab(a) \cong stab (b)$
56370
Associative operation on a set $S$
35369
Monoid / semigroup with cancellation property $ ab=ac\Rightarrow b = c,$ $\ ba = ca\Rightarrow b = c$
61394
The product of finitely many cyclic groups is cyclic
10602
Monotone Union of subgroups being subgroup
84789
Order of products of elements in a finite Abelian group