Elementary Group Theory Proof
5042
Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.
80273
Prove the centralizer of an element in group $G$ is a subgroup of $G$
128300
Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
11003
Proving that $G/N$ is an abelian group
28108
Proving the kernel is a normal subgroup.
58707
Prove Quotient Group Isomorphism
114522
Prove that identity is unique in a group
2794
Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.
103146
Proof that the Rubik’s Cube group is 2-generated
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
79452
How to prove that it is a group?
151193
Simple subgroup of Symmetric Group
154398
Show that H is a subgroup of G
90332
Prove that that $U(n)$ is an abelian group.
17510
Proving a set is an abelian group.
60208
Proof of property of abelian group
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$