Finitely presented conjugacy-separable group: Difference between revisions
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| [[Stronger than::group with solvable conjugacy problem]] || || [[finitely presented and conjugacy-separable implies solvable conjugacy problem]] || || | | [[Stronger than::group with solvable conjugacy problem]] || || [[finitely presented and conjugacy-separable implies solvable conjugacy problem]] || || | ||
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| [[Stronger than::group with solvable word problem]] || || (via solvable conjugacy problem) || || {{intermediate | | [[Stronger than::group with solvable word problem]] || || (via solvable conjugacy problem) || || {{intermediate notions short|group with solvable word problem|finitely presented conjugacy-separable group}} | ||
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| [[Stronger than::finitely generated conjugacy-separable group]] || || || || | | [[Stronger than::finitely generated conjugacy-separable group]] || || || || | ||
Latest revision as of 03:20, 1 February 2012
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) | |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 |