Is the existence of a right identity and right inverses a sufficient condition for $(G,*)$ to be a group?
17997
Right identity and Right inverse implies a group
24181
Showing that $G$ is a group under an alternative operation.
37182
If an element has a unique right inverse, is it invertible?
84397
$x$ conjugate to $y$ in a group $G$ is an equivalence relation on $G$
7973
Groups of order $pq$ have a proper normal subgroup
40094
Does $G\oplus G \cong H\oplus H$ imply $G\cong H$ in general?
40846
When can a (finite) group be written as the quotient of some other group by its center?
23279
Group Theory Isomorphism
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?
105471
How to prove that if each element of group is inverse to itself then group commutative?
124309
$g\in G$ maximal order in $G$ abelian then $G=\left\oplus H$
67554
In a group, the number of non-self-inverse elements is even
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
25439
f(a) = inverse of a is an isomorphism iff a group G is Abelian
105951
Does $G\times K\cong H\times K$ imply $G\cong H$?
14097
A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$
44258
Conditions under which group solvability is invariant under an homomorphism.