Order-dominating Hall subgroup
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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: order-dominating subgroup and Hall subgroup
View other subgroup property conjunctions | view all subgroup properties
Definition with symbols
- It is both an order-dominating subgroup and a Hall subgroup: in other words, it is a Hall subgroup such that any subgroup of whose order divides the order of is contained in some conjugate of .
- It is a -subgroup and is -dominating for some set of primes : In other words, is a -subgroup of and every -subgroup of is contained in some conjugate of .
Equivalence of definitions
For full proof, refer: Pi-dominating pi-subgroup implies pi-Hall