Locally solvable group: Difference between revisions

Latest revision as of 20:28, 22 February 2011

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 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				Solvable group\|FULL LIST, MORE INFO
solvable group				\|FULL LIST, MORE INFO
locally nilpotent group				\|FULL LIST, MORE INFO

@@ Line 8: / Line 8: @@
 {{obtainedbyapplyingthe|locally operator|solvable group}}
+==Relation with other properties==
+===Stronger properties===
+{| class="sortable" border="1"
+! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
+|-
+| [[Weaker than::abelian group]] || || || || {{intermediate notions short|locally solvable group|abelian group}}
+|-
+| [[Weaker than::nilpotent group]] || || || || {{intermediate notions short|locally solvable group|nilpotent group}}
+|-
+| [[Weaker than::solvable group]] || || || || {{intermediate notions short|locally solvable group|solvable group}}
+|-
+| [[Weaker than::locally nilpotent group]] || || || || {{intermediate notions short|locally solvable group|locally nilpotent group}}
+|}