Subnormal-permutable subnormal subgroup: Difference between revisions
(New page: {{subgroup property conjunction|subnormal-permutable subgroup|subnormal subgroup}} ==Definition== A subgroup of a group is termed a '''subnormal-permutable subnormal subgroup''' ...) |
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==Definition== | ==Definition== | ||
A [[subgroup]] of a [[group]] is termed a '''subnormal-permutable subnormal subgroup''' if it is a [[subnormal subgroup]] | A [[subgroup]] of a [[group]] is termed a '''subnormal-permutable subnormal subgroup''' if it is a [[subnormal subgroup]] as well as a [[subnormal-permutable subgroup]]: it [[permuting subgroups|permutes]] with every [[subnormal subgroup]] of the group. | ||
==Relation with other properties== | ==Relation with other properties== | ||
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* [[Stronger than::Permutable subnormal subgroup]] (for a finite group, every permutable subgroup is subnormal, so any [[permutable subgroup]] is a subnormal-permutable subnormal subgroup) | * [[Stronger than::Permutable subnormal subgroup]] (for a finite group, every permutable subgroup is subnormal, so any [[permutable subgroup]] is a subnormal-permutable subnormal subgroup) | ||
* [[Stronger than::Join-transitively subnormal subgroup]] | * [[Stronger than::Join-transitively subnormal subgroup]] | ||
* [[Stronger than::Subnormal subgroup]] | |||
Latest revision as of 13:11, 27 March 2009
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: subnormal-permutable subgroup and subnormal subgroup
View other subgroup property conjunctions | view all subgroup properties
Definition
A subgroup of a group is termed a subnormal-permutable subnormal subgroup if it is a subnormal subgroup as well as a subnormal-permutable subgroup: it permutes with every subnormal subgroup of the group.
Relation with other properties
Stronger properties
Weaker properties
- Permutable subnormal subgroup (for a finite group, every permutable subgroup is subnormal, so any permutable subgroup is a subnormal-permutable subnormal subgroup)
- Join-transitively subnormal subgroup
- Subnormal subgroup