query: If $G$ is abelian, it has a subgroup in every order of $|G|'s$ divisors?
positive_passages.docid: 152634
positive_passages.text: every Abelian group is a converse lagrange theorem group
negative_passages.docid: 98647
negative_passages.text: $G$ is Topological $\implies$ $\pi_1(G,e)$ is Abelian
negative_passages.docid: 122970
negative_passages.text: A question on $p$-groups, and order of its commutator subgroup.
negative_passages.docid: 14890
negative_passages.text: Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
negative_passages.docid: 41231
negative_passages.text: Subgroups of (Z,+) of order n
negative_passages.docid: 141890
negative_passages.text: $G$ is a Group of order $pq$, if $G$ has exactly one subgroup of order $p$ and another with order $q$, then $G$ is cyclic ($p,q$ are prime)
negative_passages.docid: 125640
negative_passages.text: Group of order $p^2$ is abelian.
negative_passages.docid: 48393
negative_passages.text: Abelian groups of order n.
negative_passages.docid: 11825
negative_passages.text: Let $H$ be a subgroup of $G$. Let $K = \{x \in G: xax^{-1} \in H \iff a \in H\}$. Prove that $K$ is a subgroup of $G$.
negative_passages.docid: 42389
negative_passages.text: If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
negative_passages.docid: 50762
negative_passages.text: If $S_n$ has cyclic subgroups of these orders or not?
negative_passages.docid: 97833
negative_passages.text: Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
negative_passages.docid: 149578
negative_passages.text: Subgroups of $(\mathbb Z_n,+)$
negative_passages.docid: 28722
negative_passages.text: Prove that $H$ is a abelian subgroup of odd order
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: 133001
negative_passages.text: $G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
negative_passages.docid: 57809
negative_passages.text: For which $n$, $G$ is abelian?