query: Automorphism groups of isomorphic groups are isomorphic
positive_passages.docid: 23579
positive_passages.text: If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
negative_passages.docid: 25439
negative_passages.text: f(a) = inverse of a is an isomorphism iff a group G is Abelian
negative_passages.docid: 157040
negative_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: 2254
negative_passages.text: Finite group with isomorphic normal subgroups and non-isomorphic quotients?
negative_passages.docid: 120288
negative_passages.text: Semigroup isomorphism
negative_passages.docid: 133664
negative_passages.text: When the automorphism group is trivial......
negative_passages.docid: 111168
negative_passages.text: Automorphisms of a finite non-abelian group
negative_passages.docid: 62035
negative_passages.text: Order of automorphism group of cyclic group
negative_passages.docid: 55393
negative_passages.text: Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
negative_passages.docid: 13761
negative_passages.text: Automorphisms in $\mathbb{Z}_n$
negative_passages.docid: 151862
negative_passages.text: Is any subgroup of a direct product isomorphic to a direct product of subgroups?
negative_passages.docid: 78553
negative_passages.text: A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$
negative_passages.docid: 55778
negative_passages.text: Group theoretic meaning of natural isomorphisms between certain functors
negative_passages.docid: 152662
negative_passages.text: Proving that any finite cyclic group of order $n$ is isomorphic to $$
negative_passages.docid: 114320
negative_passages.text: Showing that if the center of a group is trivial, then the center of its automorphism group is trivial
negative_passages.docid: 158975
negative_passages.text: Isomorphism of centers of isomorphic groups
negative_passages.docid: 87766
negative_passages.text: Using Cayley's Theorem to find an isomorphic subgroup.