query: Is Aut(G×H) isomorphic to Aut(G) × Aut(H)
positive_passages.docid: 148881
positive_passages.text: Aut(GxH) isomorphic to Aut(G)xAut(H)
negative_passages.docid: 32428
negative_passages.text: Group homomorphisms and which of the following statements are true (NBHM-$2014$)
negative_passages.docid: 65968
negative_passages.text: Prove that any two cyclic groups of the same order are isomorphic?
negative_passages.docid: 151047
negative_passages.text: a non trivial example: $G/H$ is isomorphic to $G$
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: 116168
negative_passages.text: Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$?
negative_passages.docid: 18182
negative_passages.text: An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
negative_passages.docid: 127198
negative_passages.text: What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$?
negative_passages.docid: 125982
negative_passages.text: If the dual spaces are isometrically isomorphic are the spaces isomorphic?
negative_passages.docid: 52556
negative_passages.text: Isomorphism of $S^1$.
negative_passages.docid: 128096
negative_passages.text: Let V denote the Klein 4-group. Show that $\text{Aut} (V)$ is isomorphic to $S_3$
negative_passages.docid: 69384
negative_passages.text: Are the following modules free and/or isomorphic?
negative_passages.docid: 77221
negative_passages.text: Prove that $G$ has a subgroup isomorphic to $G/H$.
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: 120288
negative_passages.text: Semigroup isomorphism
negative_passages.docid: 111024
negative_passages.text: Does $gHg^{-1}\subseteq H$ imply $gHg^{-1}= H$?
negative_passages.docid: 107687
negative_passages.text: How to prove that $U_{2^n}$ is isomorphic as group to $\mathbb Z_2 \times \mathbb Z_{2^{n-2}}$ for $n \ge 3$?