Locally solvable group
From Groupprops
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
Contents
Definition
A group is termed locally solvable if every finitely generated subgroup of it is a solvable group.
Formalisms
In terms of the locally operator
This property is obtained by applying the locally operator to the property: solvable group
View other properties obtained by applying the locally operator
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| abelian group | Solvable group|FULL LIST, MORE INFO | |||
| nilpotent group | Locally nilpotent group, Solvable group|FULL LIST, MORE INFO | |||
| solvable group | |FULL LIST, MORE INFO | |||
| locally nilpotent group | |FULL LIST, MORE INFO |
