$F$ a field and $G$ finite subset of $F \setminus \{0\}$ with 1 & satisfying $a, b ∈ G$ then $ab^{−1} ∈ G$. Show that $G$ is cyclic
8623
Finite subgroups of the multiplicative group of a field are cyclic
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
50655
Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$
152954
Extensions of finite cyclic groups
69046
Proof of $\mathbb{Q}$ is not cyclic
152071
Group $G$ is cyclic $\iff$ every subgroup of $G$ has the form $G^k$, where $G^k=\{g^k\mid g\in G\}$
18528
Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} \setminus \{-1\}$
118610
Are all extensions of finite fields cyclic?
84501
Proof involving Cyclic group, generator and GCD
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
61394
The product of finitely many cyclic groups is cyclic
14648
Show that $f_0 - f_1 + f_2 - \cdots - f_{2n-1} + f_{2n} = f_{2n-1} - 1$ when $n$ is a positive integer