query: Splitting of an exact sequence of abelian groups
positive_passages.docid: 66806
positive_passages.text: A nonsplit short exact sequence of abelian groups with $B \cong A \oplus C$
negative_passages.docid: 41731
negative_passages.text: Question about the order of the product of two elements in an abelian group
negative_passages.docid: 151830
negative_passages.text: Exact sequence splits?
negative_passages.docid: 114662
negative_passages.text: Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
negative_passages.docid: 54082
negative_passages.text: Group with exactly two subgroups of index 2
negative_passages.docid: 122335
negative_passages.text: Abelian $p$-group with unique subgroup of index $p$
negative_passages.docid: 113259
negative_passages.text: The confusing nature of direct sum for finite abelian groups
negative_passages.docid: 11003
negative_passages.text: Proving that $G/N$ is an abelian group
negative_passages.docid: 5741
negative_passages.text: Direct product of abelian groups
negative_passages.docid: 60208
negative_passages.text: Proof of property of abelian group
negative_passages.docid: 122353
negative_passages.text: Status of the classification of non-finitely generated abelian groups.
negative_passages.docid: 24966
negative_passages.text: Converse of Lagrange's theorem for abelian groups
negative_passages.docid: 116125
negative_passages.text: A group $G$ with $G'$ abelian and every abelian normal subgroup finite
negative_passages.docid: 60075
negative_passages.text: Does there exist an $n$ such that all groups of order $n$ are Abelian?
negative_passages.docid: 68971
negative_passages.text: Elementary approach to proving that a group of order 9 is Abelian
negative_passages.docid: 111746
negative_passages.text: $(A/\mathfrak{a}) \otimes_A M \simeq M / \mathfrak{a}M$ by tensoring the canonical exact sequence.
negative_passages.docid: 48393
negative_passages.text: Abelian groups of order n.