A finite, cancellative semigroup is a group
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
130792
Commutator of a group
24561
$\mathbb S_n$ as semidirect product
146952
When can I say that $\cup H_i$ is a group?
4383
Finitely generated monoids - how to show that there is not first order set axiomatizing them.
110708
On proving that a finitely generated group has a finite number of subgroups with index $n$.
17510
Proving a set is an abelian group.
33196
show that A(T) is a group under operation of composition of functions
120288
Semigroup isomorphism
152904
Groups with Same Number Of Elements and Subgroups
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
32253
How to prove $b=c$ if $ab=ac$ (cancellation law in groups)?
67554
In a group, the number of non-self-inverse elements is even
133770
Subgroups of finite abelian groups.
21243
Kaplansky's theorem of infinitely many right inverses in monoids?
145159
Finite group is abelian if the representatives of its conjugacy classes commute
68732
Prove that a semigroup satisfying $a^pb^q=ba$ is commutative