Show that $G$ is a group if the cancellation law holds when identity element is not sure to be in $G$
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
63359
Show that the product of all group elements is $e$ or $u$ if $G$ has exactly one involution $u$
135701
An example of a group such that $G \cong G \times G$
118022
Show that a group of order $180$ is not simple.
103216
The set $\{g^2 | g \in G\}$ in a group $G$
142228
Proof that a subset closed under group operation of a finite group is a subgroup
101596
Determine group G as cyclic
5089
An element of a group has the same order as its inverse
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
90584
Show set of affine transformations is a group
60208
Proof of property of abelian group
140334
Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.
71420
Prove that a group is abelian.
90081
problems in group theory
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
142739
Nonempty subset H of group G is subgroup iff $ab^{-1} \in H $ for any $a,b \in H$