query: A problem about abelian group
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: 51352
negative_passages.text: Subgroups of a finite abelian group
negative_passages.docid: 88718
negative_passages.text: A group is generated by two elements of order $2$ is infinite and non-abelian
negative_passages.docid: 138862
negative_passages.text: Product of all elements in an odd finite abelian group is 1
negative_passages.docid: 48585
negative_passages.text: Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
negative_passages.docid: 125640
negative_passages.text: Group of order $p^2$ is abelian.
negative_passages.docid: 1577
negative_passages.text: Order of nontrivial elements is 2 implies Abelian group
negative_passages.docid: 96878
negative_passages.text: A finite group with the property that all of its proper subgroups are abelian
negative_passages.docid: 39895
negative_passages.text: Showing a free abelian group is generated by its basis
negative_passages.docid: 133770
negative_passages.text: Subgroups of finite abelian groups.
negative_passages.docid: 90811
negative_passages.text: If $[G' : G'']\leq p^2$, then $G'$ is abelian.
negative_passages.docid: 5741
negative_passages.text: Direct product of abelian groups
negative_passages.docid: 88726
negative_passages.text: Problem about solvable groups
negative_passages.docid: 13355
negative_passages.text: Product of elements of a finite abelian group
negative_passages.docid: 109611
negative_passages.text: If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
negative_passages.docid: 13631
negative_passages.text: Showing group with $p^2$ elements is Abelian
negative_passages.docid: 35913
negative_passages.text: Abelianization of free group is the free abelian group