Order-dominating subgroup
From Groupprops
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Contents
Definition
Symbol-free definition
A finite subgroup of a group is termed order-dominating if every other subgroup whose order divides its order, is conjugate to a subgroup contained in it.
Definition with symbols
Let be a group and
be a finite subgroup. Then,
is termed order-dominating in
if, for any subgroup
such that the order of
divides the order of
, there exists
such that
.
Relation with other properties
Stronger properties
- Sylow subgroup (in a finite group)
- Hall subgroup in a finite solvable group