Finitely generated profinite group: Difference between revisions
(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) | |FULL LIST, MORE INFO | |
| Residually finite group | |FULL LIST, MORE INFO | |||
| Hopfian group | |FULL LIST, MORE INFO | |||
| Finitely generated group | |FULL LIST, MORE INFO | |||
| Profinite group | |FULL LIST, MORE INFO |