Maximal subgroup of finite nilpotent group: Difference between revisions
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{{subgroup property}} | {{in-group subgroup property|maximal subgroup|finite nilpotent group}} | ||
==Definition== | ==Definition== | ||
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Weaker than::Characteristic maximal subgroup | * [[Weaker than::Characteristic maximal subgroup of finite nilpotent group]] | ||
* [[Weaker than::Maximal subgroup of group of prime power order]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
* [[Stronger than::Maximal subgroup | * [[Stronger than::Maximal subgroup of nilpotent group]] | ||
* [[Stronger than::Maximal normal subgroup]] | * [[Stronger than::Maximal normal subgroup]] | ||
* [[Stronger than::Normal subgroup of prime index]] | * [[Stronger than::Normal subgroup of prime index]] | ||
* [[Stronger than::Maximal subgroup]] | * [[Stronger than::Maximal subgroup]] | ||
* [[Stronger than::Normal subgroup]] | * [[Stronger than::Normal subgroup]] | ||
* [[Stronger than::Order-normal subgroup]] | |||
* [[Stronger than::Isomorph-normal subgroup]] | * [[Stronger than::Isomorph-normal subgroup]] | ||
Latest revision as of 15:10, 5 August 2009
This article describes a property that arises as the conjunction of a subgroup property: maximal subgroup with a group property imposed on the ambient group: finite nilpotent group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup
Definition
A maximal subgroup in finite nilpotent group is the following equivalent things:
- A maximal subgroup of a finite nilpotent group.
- A maximal normal subgroup of a finite nilpotent group.
- A subgroup of prime index of a finite nilpotent group.
Relation with other properties
Stronger properties
- Characteristic maximal subgroup of finite nilpotent group
- Maximal subgroup of group of prime power order