query: Group isomorphism with a fixed element
positive_passages.docid: 24181
positive_passages.text: Showing that $G$ is a group under an alternative operation.
negative_passages.docid: 36882
negative_passages.text: Two finite abelian groups with the same number of elements of any order are isomorphic
negative_passages.docid: 27728
negative_passages.text: Question on a homomorphism of a set G.
negative_passages.docid: 33868
negative_passages.text: A transformation between two free group actions.
negative_passages.docid: 101064
negative_passages.text: Showing the triviality of homomorphisms
negative_passages.docid: 54082
negative_passages.text: Group with exactly two subgroups of index 2
negative_passages.docid: 56234
negative_passages.text: Isomorphism $f$ preserves the order of an element?
negative_passages.docid: 98734
negative_passages.text: Order of a product of elements in a generic group
negative_passages.docid: 25728
negative_passages.text: A second isomorphism theorem for action on cosets
negative_passages.docid: 23579
negative_passages.text: If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
negative_passages.docid: 933
negative_passages.text: How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
negative_passages.docid: 28210
negative_passages.text: A finite group with exactly $2$ conjugacy classes isomorphic to $\mathbb{Z}_2$
negative_passages.docid: 120288
negative_passages.text: Semigroup isomorphism
negative_passages.docid: 90192
negative_passages.text: Kernel and Image of a group homomorphism
negative_passages.docid: 32428
negative_passages.text: Group homomorphisms and which of the following statements are true (NBHM-$2014$)
negative_passages.docid: 33294
negative_passages.text: The correspondence theorem for groups
negative_passages.docid: 84132
negative_passages.text: Number of preimages of a group element under a homomorphism.