Group with a finite complete rewriting system: Difference between revisions
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| [[Weaker than::finitely generated abelian group]] || || || || {{intermediate notions short|group with a finite complete rewriting system|finitely generated abelian group}} | | [[Weaker than::finitely generated abelian group]] || || || || {{intermediate notions short|group with a finite complete rewriting system|finitely generated abelian group}} | ||
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| [[Weaker than::finitely generated nilpotent group]] || || || || {{intermediate notions short|group with a finite complete rewriting system|finitely generated nilpotent group}} | |||
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| [[Weaker than::finite group]] || || || || {{intermediate notions short|group with a finite complete rewriting system|finite group}} | | [[Weaker than::finite group]] || || || || {{intermediate notions short|group with a finite complete rewriting system|finite group}} | ||
Latest revision as of 05:38, 28 July 2013
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
Definition
A finitely generated group is termed a group with a finite complete rewriting system if it has a complete rewriting system (i.e., a rewriting system that is both finitely terminating and confluent) with respect to a finite generating set such that the rewriting system is finite in size, i.e., it makes use of only finitely many rewriting rules.
Note that it is possible for a group to have a finite complete rewriting system with respect to one finite generating set but not have any finite complete rewriting system with respect to a different finite generating set. We use the term group with a finite complete rewriting system if there exists at least one finite generating set for which a finite complete rewriting system exists.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| finitely generated free group | |FULL LIST, MORE INFO | |||
| finitely generated abelian group | |FULL LIST, MORE INFO | |||
| finitely generated nilpotent 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 word problem | ||||
| finitely generated group |