Hall retract
From Groupprops
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: Hall subgroup and retract
View other subgroup property conjunctions | view all subgroup properties
Contents
Definition
A Hall retract of a finite group is a Hall subgroup that is also a retract: in other words, it possesses a normal complement. Note that the normal complement must also be a Hall subgroup, and in fact, a normal Hall subgroup.
Relation with other properties
Stronger properties
Weaker properties
- Order-conjugate subgroup
- Order-isomorphic subgroup
- Order-automorphic subgroup
- Isomorph-automorphic subgroup
- Isomorph-conjugate subgroup
- Automorph-conjugate subgroup
- Procharacteristic subgroup
- Pronormal subgroup
- Intermediately isomorph-conjugate subgroup
- Intermediately automorph-conjugate subgroup
- Intermediately normal-to-characteristic subgroup
- Intermediately subnormal-to-normal subgroup