Prove that a set of nonzero real numbers is a group under the operation $a*b$
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
116009
Proving that if a set is both open and closed then it is equal to the real numbers
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
22232
Proving that cardinality of the reals = cardinality of $[0,1]$
43759
Prove that the set $\mathrm{Aut}(G)$ of all automorphisms of the group $G$ with the operation of taking the composition is a group
3462
Proving a set of automorphisms of a group is a group under composition
50266
In the following figure prove that: $AK||BC$
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.
56370
Associative operation on a set $S$
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
41052
The set of real numbers and power set of the natural numbers
22783
Is the set $Z_n = \{ 0, 1, . . . , n-1 \}$ for $n ≥ 1$ is a group under addition modulo n?
84198
Step in Proof of Cardinality of Product of two Groups
99346
Prove a result on transitive group actions.
157841
Existence of a non-abelian group of order $p^n$.
114662
Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
135814
Prove certain subsets of $\mathbb R^n$ are subspaces