query: Show that $H = \{g ∈ G : \hbox{|g| is finite}\}$ is a subgroup
positive_passages.docid: 145563
positive_passages.text: In an abelian group, the elements of finite order form a subgroup.
negative_passages.docid: 55350
negative_passages.text: H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
negative_passages.docid: 102912
negative_passages.text: Subgroups of finitely generated groups are not necessarily finitely generated
negative_passages.docid: 97928
negative_passages.text: Normal subgroup of a normal subgroup
negative_passages.docid: 42891
negative_passages.text: Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
negative_passages.docid: 34724
negative_passages.text: For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
negative_passages.docid: 64408
negative_passages.text: Subgroup of $\mathbb{Q}$ with finite index
negative_passages.docid: 129753
negative_passages.text: Prove that a subgroup which contains half of all elements is a normal subgroup.
negative_passages.docid: 61064
negative_passages.text: Finite index subgroup $G$ of $\mathbb{Z}_p$ is open.
negative_passages.docid: 1220
negative_passages.text: Have $\alpha:G \to H$. If a subgroup $U$ is normal in $H$ prove the pre-image of $U$ is normal in $G$.
negative_passages.docid: 141043
negative_passages.text: $H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
negative_passages.docid: 56245
negative_passages.text: Let H be a subgroup of a group G. Prove that the following statements are equivalent.
negative_passages.docid: 138297
negative_passages.text: Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
negative_passages.docid: 106277
negative_passages.text: Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
negative_passages.docid: 34567
negative_passages.text: If $G_1$ and $G_2$ are finite group and $H\leq G_1\times G_2$ then $H=P_1\times P_2$ with $P_i\leq G_i$?
negative_passages.docid: 132342
negative_passages.text: Suppose $H$ is a subgroup of $S_n$ but $H$ is not a subgroup of $A_n$. Prove that |$H$ ∩ $A_n$| = $\frac{1}{2}|H|$?
negative_passages.docid: 150199
negative_passages.text: How to prove for a finite group that $|\langle g \rangle|=o(g)$?