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

From Groupprops

The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter

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## Statement

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