Finitely presented conjugacy-separable group

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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
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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