Proving $G$ is a group if it is closed under product and both cancellation laws hold.
6755
A finite, cancellative semigroup is a group
34966
Is the product of closed subgroups in topological group closed?
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
80273
Prove the centralizer of an element in group $G$ is a subgroup of $G$
52095
Prove either $G=ST$ or |$G|\geq|S|+|T|$
84198
Step in Proof of Cardinality of Product of two Groups
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
143457
Is product of two closed sets closed?
30676
$G'$ and the product of all the elements in an odd order group
36709
subgroup of direct product of two groups
43759
Prove that the set $\mathrm{Aut}(G)$ of all automorphisms of the group $G$ with the operation of taking the composition is a group
116707
Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
60208
Proof of property of abelian group
70034
Showing that this set of functions is a group.
22477
If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK.
5599
Proving an inclusion for the derived group
14097
A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$