Group in which every p-local subgroup is p-constrained

From Groupprops
Jump to: navigation, search
The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter
View other prime-parametrized group properties | View other group properties

Statement

Suppose G is a finite group and p is a prime number. We say that G is a group in which every p-local subgroup is p-constrained if any p-local subgroup (i.e., the normalizer of any non-identity p-subgroup) of G is a p-constrained group.

Facts

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Group in which every p-local subgroup is p-solvable every p-local subgroup is a p-solvable group (for that specific prime number p) follows from p-solvable implies p-constrained |FULL LIST, MORE INFO
N-group (finite) every local subgroup (normalizer of a nontrivial solvable subgroup) is solvable Group in which every p-local subgroup is p-solvable|FULL LIST, MORE INFO
minimal simple group (finite) simple non-abelian group in which every proper subgroup is solvable N-group|FULL LIST, MORE INFO
p-solvable group
finite solvable group
p-nilpotent group
finite nilpotent group