Finitely presented conjugacy-separable group
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Contents
Definition
A finitely presented conjugacy-separable group is a group that is both finitely presented and conjugacy-separable.
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: finitely presented group and conjugacy-separable group
View other group property conjunctions OR view all group properties
Relation with other properties
Stronger properties
Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|
finitely generated abelian group | |FULL LIST, MORE INFO | |||
finitely generated free group | |FULL LIST, MORE INFO | |||
finite group | |FULL LIST, MORE INFO |
Weaker properties
Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|
group with solvable conjugacy problem | finitely presented and conjugacy-separable implies solvable conjugacy problem | |||
group with solvable word problem | (via solvable conjugacy problem) | Finitely presented residually finite group, Group with solvable conjugacy problem|FULL LIST, MORE INFO | ||
finitely generated conjugacy-separable group | ||||
conjugacy-separable group | ||||
finitely presented group | ||||
finitely presented residually finite group | ||||
finitely generated residually finite group | ||||
residually finite group | ||||
Hopfian group | via finitely generated residually finite | |||
finitely generated Hopfian group | ||||
finitely generated group |