A finite semigroup with left and right cancellation is a group.
6755
A finite, cancellative semigroup is a group
24181
Showing that $G$ is a group under an alternative operation.
71420
Prove that a group is abelian.
96614
Finite number of subgroups $\Rightarrow$  finite group
147013
Subset of a finite set is finite
3104
Prove that a group is infinite and nonabelian.
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
157765
What would a Cayley table of inverse semigroup look like?
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
148992
A finite set is closed
109470
Proof of whether a specific element is in a commutative, invertible monoid.
65900
Show that a finite group with certain automorphism is abelian
146952
When can I say that $\cup H_i$ is a group?
16476
Order of the product of two commuting elements with coprime orders in a group.
121141
Proving Finiteness of Group from Presentation
4383
Finitely generated monoids - how to show that there is not first order set axiomatizing them.
48009
Left inverse implies right inverse in a finite ring