query: New Criteria of Isomorphism + Abelian Group
positive_passages.docid: 29051
positive_passages.text: If I know the order of every element in a group, do I know the group?
negative_passages.docid: 151047
negative_passages.text: a non trivial example: $G/H$ is isomorphic to $G$
negative_passages.docid: 59811
negative_passages.text: Finite Abelian groups with the same number of elements for all orders are isomorphic
negative_passages.docid: 134858
negative_passages.text: Abelian Group Homomorphism
negative_passages.docid: 115663
negative_passages.text: Proving an isomorphism using the isomorphism theorems
negative_passages.docid: 3907
negative_passages.text: Abelian quotient group
negative_passages.docid: 137896
negative_passages.text: Isomorphism equivalence implies fundamental group is abelian
negative_passages.docid: 30236
negative_passages.text: isomorphic groups related in direct product.
negative_passages.docid: 46263
negative_passages.text: Automorphisms of infinite abelian groups
negative_passages.docid: 150204
negative_passages.text: Isomorphisms between the groups $U(10), U(5)$ and $\mathbb{Z}/4\mathbb{Z}$
negative_passages.docid: 93169
negative_passages.text: Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
negative_passages.docid: 48585
negative_passages.text: Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
negative_passages.docid: 37928
negative_passages.text: Isomorphism between $D_{2n}/Z(D_{2n})$ and $D_n$
negative_passages.docid: 13631
negative_passages.text: Showing group with $p^2$ elements is Abelian
negative_passages.docid: 5906
negative_passages.text: All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $
negative_passages.docid: 108213
negative_passages.text: $N_1,N_2,N_3 \unlhd G, N_i\cap N_j =\{e\}, G = N_iN_j$. Want to show that $G$ is abelian, $N_i$ are isomorphic.
negative_passages.docid: 122353
negative_passages.text: Status of the classification of non-finitely generated abelian groups.