query: Is there non-trivial examples for groups $G$ satisfying $G = \mathrm{Aut}(G)$
positive_passages.docid: 152603
positive_passages.text: Group isomorphic to its automorphism group
negative_passages.docid: 121034
negative_passages.text: Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
negative_passages.docid: 3756
negative_passages.text: If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
negative_passages.docid: 150585
negative_passages.text: Group with $a=a^{-1}$ for all $a\in G$ is abelian
negative_passages.docid: 103423
negative_passages.text: Normal subgroup where G has order prime
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: 101079
negative_passages.text: Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
negative_passages.docid: 116737
negative_passages.text: An element of a group $G$ is not conjugate to its inverse if $\lvert G\rvert$ is odd
negative_passages.docid: 107511
negative_passages.text: If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?
negative_passages.docid: 151047
negative_passages.text: a non trivial example: $G/H$ is isomorphic to $G$
negative_passages.docid: 112263
negative_passages.text: an example for $\pi$-quasinormal subgroup but is not normal
negative_passages.docid: 57883
negative_passages.text: Example of a Subgroup That Is Not Normal
negative_passages.docid: 99538
negative_passages.text: Non-trivial groups pairwise non-isomorphic with isomorphic direct products
negative_passages.docid: 56650
negative_passages.text: Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
negative_passages.docid: 34606
negative_passages.text: Which groups have precisely two automorphisms
negative_passages.docid: 35353
negative_passages.text: Isomorphic quotient groups $\frac{G}{H} \cong \frac{G}{K}$ imply $H \cong K$?
negative_passages.docid: 150961
negative_passages.text: An example for a homomorphism that is not an automorphism