For $A,B \in \mathscr{M}_{2\times2}(\mathbb{Q}) $ of finite order, show that $AB$ has infinite order
8742
Examples and further results about the order of the product of two elements in a group
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
1577
Order of nontrivial elements is 2 implies Abelian group
129750
Order of $SL_2(\mathbb{Z}/ n\mathbb{Z})$
26398
Group of even order contains an element of order 2
131163
There is a well ordering of the class of all finite sequences of ordinals
71608
A property of finite field of order $2^n$
29445
Trying to prove that $H=\langle a,b:a^{3}=b^{3}=(ab)^{3}=1\rangle$ is a group of infinite order.
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
140430
Let $E = \mathbb{Q}\big(\left\{\sqrt[n]{2} \mid n \in \mathbb{N} \setminus \left\{0\right\} \right\} \big)$. Prove $[E: \mathbb{Q}]$ is not finite
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
151544
Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$
33300
Showing order of $Z (G) =1$ or $pq$
104513
Order of elements in $Z_n$
62977
Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
50266
In the following figure prove that: $AK||BC$
25488
Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.