query: condition for a group to be abelian
positive_passages.docid: 26148
positive_passages.text: A group such that $a^m b^m = b^m a^m$ and $a^n b^n = b^n a^n$ ($m$, $n$ coprime) is abelian?
negative_passages.docid: 119512
negative_passages.text: If H ≤ Z(G) ≤ G, where G is a finite group,Z(G) is its center, and (G:H) = p for some prime p, then G is abelian.
negative_passages.docid: 71035
negative_passages.text: Non abelian subgroup of a abelian group.
negative_passages.docid: 152630
negative_passages.text: showing that a group of order 45 is abelian
negative_passages.docid: 85508
negative_passages.text: Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
negative_passages.docid: 41731
negative_passages.text: Question about the order of the product of two elements in an abelian group
negative_passages.docid: 98542
negative_passages.text: Prove that $H$ is a subgroup of an abelian group $G$
negative_passages.docid: 3907
negative_passages.text: Abelian quotient group
negative_passages.docid: 97565
negative_passages.text: Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
negative_passages.docid: 84789
negative_passages.text: Order of products of elements in a finite Abelian group
negative_passages.docid: 152820
negative_passages.text: Every element of a group has order $2$. Why, intuitively, is it abelian?
negative_passages.docid: 135039
negative_passages.text: ${\rm Aut}(G)$ is cyclic $\implies G$ is abelian
negative_passages.docid: 108425
negative_passages.text: Problem on abelian group
negative_passages.docid: 15341
negative_passages.text: Non-abelian finite group in which more than half of the elements have order $2$
negative_passages.docid: 60208
negative_passages.text: Proof of property of abelian group
negative_passages.docid: 73571
negative_passages.text: Proof of Cauchy's Theorem for abelian groups
negative_passages.docid: 17510
negative_passages.text: Proving a set is an abelian group.