$[G : H] < ∞$ and$ [G : K] < ∞$ then $[G : H ∩ K] < ∞$ where $H$ and $K$ be subgroups of $G$
46121
Does the intersection of two finite index subgroups have finite index?
43750
Subgroups of finite solvable groups. Solvable?
11957
G is the product of its Sylow subgroups
101345
Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
133770
Subgroups of finite abelian groups.
98765
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
124709
Suppose G be a non-abelian group and H,K be two abelian subgroups of G. Then must HK be an abelian subgroup of G?
139451
Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
93666
Does the closedness of a subgroup $H$ of $G$ imply that for $h\in H, g\in G \setminus H : hg \not \in H$?
70373
Intersection of normal subgroups proof
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
150042
Prove $x^{-1}Hx$ is a subgroup of $G$
68955
Characterising subgroups of Prüfer $p$-groups.
151130
When is the product of $n$ subgroups a subgroup?
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
72150
Union of the conjugates of a proper subgroup
61379
Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$.