query: Show the map from the product of disjoint subgroups of G to G is an isomorphism
positive_passages.docid: 23279
positive_passages.text: Group Theory Isomorphism
negative_passages.docid: 152212
negative_passages.text: Prove that the natural map $\alpha : \text{Hom}(X,\text{Spec} A) \rightarrow \text{Hom}(A,\Gamma(X,\mathcal{O}_X))$ is an isomorphism
negative_passages.docid: 73988
negative_passages.text: Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$
negative_passages.docid: 151699
negative_passages.text: Group of inner automorphisms of a group $G$
negative_passages.docid: 121449
negative_passages.text: An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$
negative_passages.docid: 63359
negative_passages.text: Show that the product of all group elements is $e$ or $u$ if $G$ has exactly one involution $u$
negative_passages.docid: 115663
negative_passages.text: Proving an isomorphism using the isomorphism theorems
negative_passages.docid: 90584
negative_passages.text: Show set of affine transformations is a group
negative_passages.docid: 158975
negative_passages.text: Isomorphism of centers of isomorphic groups
negative_passages.docid: 70904
negative_passages.text: Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups
negative_passages.docid: 107716
negative_passages.text: Show that $G$ is cyclic
negative_passages.docid: 25728
negative_passages.text: A second isomorphism theorem for action on cosets
negative_passages.docid: 132127
negative_passages.text: Proving a direct product of groups is a group
negative_passages.docid: 97608
negative_passages.text: Showing a Ring of endomorphisms is isomorphic to a Ring
negative_passages.docid: 102622
negative_passages.text: K is a subgroup of G. Show that K is not a normal subgroup
negative_passages.docid: 13453
negative_passages.text: Bijection map from a set of subgroup to another set of subgroup under some condition.
negative_passages.docid: 103106
negative_passages.text: Proving that any permutation in $S_n$ can be written as a product of disjoint cycles