Order-normal subgroup
From Groupprops
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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]
Definition
A finite subgroup of a group
is termed an order-normal subgroup if every subgroup of
having the same order as
is a normal subgroup of
.
Relation with other properties
Stronger properties
- Order-unique subgroup
- Normal Hall subgroup
- Normal Sylow subgroup
- Maximal subgroup of group of prime power order
- Maximal subgroup of finite nilpotent group