Permutably complemented Hall subgroup
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: permutably complemented subgroup and Hall subgroup
View other subgroup property conjunctions | view all subgroup properties
- is a Hall subgroup of : the order and index of are relatively prime.
- is a permutably complemented subgroup of : there exists a subgroup of such that is trivial and (in other words, and are permutable complements). Note that also must be a Hall subgroup of : if is -Hall, is -Hall.
Relation with other properties
- Hall retract
- Normal Hall subgroup: For full proof, refer: Normal Hall implies permutably complemented
- Hall direct factor