query: If two internal products are isomorphic and one of each are isomorphic then the others are isomorphic
positive_passages.docid: 18247
positive_passages.text: Cancellation of Direct Products
negative_passages.docid: 155669
negative_passages.text: $\mathrm{Aut}(D_4)$ is isomorphic to $D_4$
negative_passages.docid: 151047
negative_passages.text: a non trivial example: $G/H$ is isomorphic to $G$
negative_passages.docid: 132487
negative_passages.text: Proving that if $V$ is an inner product space and $U_1, U_2$ are subsets, then $U_1 \subset U_2$ if and only if $U^{\perp}_2 \subset U^{\perp}_1$
negative_passages.docid: 151862
negative_passages.text: Is any subgroup of a direct product isomorphic to a direct product of subgroups?
negative_passages.docid: 145700
negative_passages.text: Module isomorphic to second dual
negative_passages.docid: 18540
negative_passages.text: Isomorphism from $\mathbb{C}[G]$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.
negative_passages.docid: 99538
negative_passages.text: Non-trivial groups pairwise non-isomorphic with isomorphic direct products
negative_passages.docid: 140865
negative_passages.text: Rings' second isomorphism theorem
negative_passages.docid: 65968
negative_passages.text: Prove that any two cyclic groups of the same order are isomorphic?
negative_passages.docid: 42579
negative_passages.text: Composition of 2 involutions
negative_passages.docid: 154754
negative_passages.text: Is $O_n$ isomorphic to $SO_n \times \{\pm I\}$?
negative_passages.docid: 120035
negative_passages.text: Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
negative_passages.docid: 115663
negative_passages.text: Proving an isomorphism using the isomorphism theorems
negative_passages.docid: 102371
negative_passages.text: Proving that two vector spaces of equal dimension are isomorphic
negative_passages.docid: 25728
negative_passages.text: A second isomorphism theorem for action on cosets
negative_passages.docid: 86025
negative_passages.text: Nonabelian semidirect products of order $pq$?