Consider $a,b\in \Bbb Z_n$ such that $o(a)=r,o(b)=s$. If $s\mid r$ then $b\in \langle a\rangle $.
39938
Subgroups of a cyclic group and their order.
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
89192
$(\mathbb R, \oplus)$ is a group. Define a multiplication with which we get a field. Where $a \oplus b = a + b +1$
21006
Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?
8920
There exists $C\neq0$ with $CA=BC$ iff $A$ and $B$ have a common eigenvalue
2626
Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
18528
Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} \setminus \{-1\}$
29445
Trying to prove that $H=\langle a,b:a^{3}=b^{3}=(ab)^{3}=1\rangle$ is a group of infinite order.
80601
Let $a,b$ be in a group $G$. Show $(ab)^n=a^nb^n$ $\forall n\in\mathbb{Z}$ if and only if $ab=ba$.
78298
On the nilpotence of the matrix $AB-BA$
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
57166
Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
98352
If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
14403
If $n = p_1^{a_1} ... p_r^{a_r}$ the set of nilpotents of $\mathbb{Z}_n$ is $(p_1 p_2 ... p_{r-1} p_r)\Bbb Z_n$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
102990
Prove or disprove: $S_{10} = \langle (1,3),(1,2, ... ,10) \rangle$