Proving uniqueness (basics of group theory)
114522
Prove that identity is unique in a group
40513
A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
70034
Showing that this set of functions is a group.
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
33387
Proof that $n\Bbb Z \leq \Bbb Z$ and are the only subgroups of $\Bbb Z$
133298
Assume $|G|=40$. Show that the subgroup of order $8$ is normal and unique.
5599
Proving an inclusion for the derived group
34099
Proving that the empty set is unique
63359
Show that the product of all group elements is $e$ or $u$ if $G$ has exactly one involution $u$
24181
Showing that $G$ is a group under an alternative operation.
114320
Showing that if the center of a group is trivial, then the center of its automorphism group is trivial
98542
Prove that $H$ is a subgroup of an abelian group $G$
56650
Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
99205
Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
3632
Basic number theory proofs
45770
Does the order, lattice of subgroups, and lattice of factor groups, uniquely determine a group up to isomorphism?
23517
Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group