If $G_1, G_2$ are two nonzero subgroups of $(\mathbb{Q},+)$, prove that $G_1\cap G_2\neq\{0\} $.
139451
Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
52105
Prove that $HK$ is a subgroup iff $HK=KH$.
97928
Normal subgroup of a normal subgroup
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
75068
subgroups of $\mathbb Z / 2 \mathbb Z \times \mathbb Z / 2 \mathbb Z$
156941
Subgroups of $\mathbb{Z}$
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
3317
Subgroup generated by $2$ and $7$ in $(\mathbb Z,+)$
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
24951
Suppose $f_1 \in \Theta(g_1) \land f_2 \in \Theta(g_2)$. Prove $f_1 + f_2 \in \Theta(\max\{g_1, g_2\})$.
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
85882
Show that $1\otimes (1,1,\ldots)\neq 0$ in $\mathbb{Q} \otimes_{\mathbb{Z}} \prod_{n=2}^{\infty} (\mathbb{Z}/n \mathbb{Z})$.
119758
On the order of elements of $\mathrm{GL}(2,q)$.
51352
Subgroups of a finite abelian group