Find a generator of the intersection of two cyclic subgroups, $\langle a^m\rangle\cap\langle a^n\rangle$
2626
Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$
158074
Cyclic group $G$ with generator $ab$.
147298
How to find all subgroups of a direct product?
106653
How many generator has a cyclic group of order n?
134687
Is there a more elegant way of proving $\langle (1,2)(3,4), (1,2,3,4,5) \rangle = A_5$
96680
Generators of symmetric group $S_n$
74077
A intersection (A union B)
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
76504
Non-trivial cyclic group with unique generator
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
98352
If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
151621
$G$ a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K = \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$
128710
Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
47522
group generators of $(\mathbb Z_{17}-\{0\},\times)$
56800
Intersection of prime ideals
98474
Show the existence of a certain subgroup of F2