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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.
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RANDOM TIP:The metaproperties section lists important facts about the subgroup property, and addresses many of the natural questions that arise about it. It has links to proofs.
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 G be a group and H be a finite subgroup. Then, H is termed order-dominating in G if, for any subgroup
such that the order of K divides the order of G, there exists
such that
.
Relation with other properties
Stronger properties
- Sylow subgroup (in a finite group)
- Hall subgroup in a finite solvable group
Weaker properties
Facts about Order-dominating subgroupRDF feed
| Stronger than | Order-conjugate subgroup + |
| Weaker than | Sylow subgroup + |

