Prove a group is equal to its commutator subgroup
8483
A Particular Two-Variable System in a Group
92873
To prove in a Group Left identity and left inverse implies right identity and right inverse
2174
Proving that HK is a subgroup when K is normal
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
128300
Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
88199
The commutator subgroup of a quotient in terms of the commutator subgroup and the kernel
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
65744
How can I Prove that H=G or K=G
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
3456
Commutator of two normal subgroups with trivial intersections
101543
Let $A$ be a group, where $a^2=1$, a belongs to $A$. Prove that this group is commutative.
87946
Proving that the unities of a ring form a group under multiplication
11003
Proving that $G/N$ is an abelian group
63359
Show that the product of all group elements is $e$ or $u$ if $G$ has exactly one involution $u$
60208
Proof of property of abelian group
4883
Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$