query: Cancellation for finitely generated abelian groups
positive_passages.docid: 157040
positive_passages.text: For groups $A,B,C$, if $A\times B$ and $A\times C$ are isomorphic do we have $B$ isomorphic to $C$?
negative_passages.docid: 10816
negative_passages.text: Infinitely generated subgroup of a finitely one (weird)
negative_passages.docid: 75970
negative_passages.text: $\mathbb Z[1/2]$ is not finitely generated?
negative_passages.docid: 42652
negative_passages.text: Must $k$-subalgebra of $k[x]$ be finitely generated?
negative_passages.docid: 13834
negative_passages.text: Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
negative_passages.docid: 113936
negative_passages.text: Showing that a finite abelian group has a subgroup of order m for each divisor m of n
negative_passages.docid: 126426
negative_passages.text: Does every infinite finitely generated group contains an element of infinite period?
negative_passages.docid: 93029
negative_passages.text: Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
negative_passages.docid: 48393
negative_passages.text: Abelian groups of order n.
negative_passages.docid: 121707
negative_passages.text: Generating Elements of Galois Group
negative_passages.docid: 65900
negative_passages.text: Show that a finite group with certain automorphism is abelian
negative_passages.docid: 158074
negative_passages.text: Cyclic group $G$ with generator $ab$.
negative_passages.docid: 116125
negative_passages.text: A group $G$ with $G'$ abelian and every abelian normal subgroup finite
negative_passages.docid: 17510
negative_passages.text: Proving a set is an abelian group.
negative_passages.docid: 18182
negative_passages.text: An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
negative_passages.docid: 152363
negative_passages.text: Cancellation in topological product
negative_passages.docid: 133770
negative_passages.text: Subgroups of finite abelian groups.