Difference between revisions of "Finitely generated profinite group"

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(Created page with '{{group property conjunction|finitely generated group|profinite group}} ==Definition== A '''finitely generated profinite group''' is a group that is both a [[finitely gener...')
 
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| [[Stronger than::Finitely generated group]] || || || || {{intermediate notions short|finitely generated group|finitely generated profinite group}}
 
| [[Stronger than::Finitely generated group]] || || || || {{intermediate notions short|finitely generated group|finitely generated profinite group}}
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| [[Stronger than::Profinite group]] || || || || {{intermediate notions short|profinite group|finitely generated profinite group}}
 
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Latest revision as of 02:54, 20 May 2010

This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: finitely generated group and profinite group
View other group property conjunctions OR view all group properties

Definition

A finitely generated profinite group is a group that is both a finitely generated group and a profinite group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finite group finitely generated and profinite not implies finite |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finitely generated residually finite group finitely generated and residually finite profinite implies residually finite |FULL LIST, MORE INFO
Finitely generated Hopfian group finitely generated and Hopfian (via residually finite) Finitely generated residually finite group|FULL LIST, MORE INFO
Residually finite group Finitely generated residually finite group, Profinite group|FULL LIST, MORE INFO
Hopfian group Finitely generated residually finite group|FULL LIST, MORE INFO
Finitely generated group Finitely generated residually finite group|FULL LIST, MORE INFO
Profinite group |FULL LIST, MORE INFO