Finitely generated parafree group
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: finitely generated group and parafree group
View other group property conjunctions OR view all group properties
Definition
A group is termed a finitely generated parafree group if it is both a finitely generated group and a parafree group. Note that the free group that this finitely generated parafree group has the same lower central series as is a finitely generated free group, and further, its rank is determined by the isomorphism type of the parafree group (explicitly, it equals the rank of the abelianization of the parafree group).
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| finitely generated free group | immediate | finitely generated and parafree not implies free | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| parafree group | |FULL LIST, MORE INFO | |||
| residually nilpotent group | |FULL LIST, MORE INFO | |||
| finitely generated residually nilpotent group | |FULL LIST, MORE INFO |