Join-transitively 2-subnormal subgroup: Difference between revisions
(New page: {{wikilocal}} {{subgroup property}} ==Definition== ===Symbol-free definition=== A subgroup of a group is termed '''join-transitively 2-subnormal''' if its [[join of subgroups|jo...) |
|||
| (One intermediate revision by the same user not shown) | |||
| Line 10: | Line 10: | ||
Note that this is ''strictly'' stronger than the property of being 2-subnormal, because [[2-subnormality is not finite-join-closed]]. | Note that this is ''strictly'' stronger than the property of being 2-subnormal, because [[2-subnormality is not finite-join-closed]]. | ||
==Formalisms== | |||
{{obtainedbyapplyingthe|join-transiter|2-subnormal subgroup}} | |||
==Relation with other properties== | ==Relation with other properties== | ||
| Line 18: | Line 21: | ||
===Weaker properties=== | ===Weaker properties=== | ||
* [[Stronger than::2-subnormal subgroup]] | * [[Stronger than::2-subnormal subgroup]]: Also related: | ||
* [[Stronger than::Join-transitively subnormal subgroup]] | ** [[Stronger than::Join-transitively subnormal subgroup]] | ||
** [[Stronger than::Subnormal subgroup]] | |||
==Metaproperties== | ==Metaproperties== | ||
{{finite-join-closed}} | {{finite-join-closed}} | ||
Latest revision as of 13:10, 27 March 2009
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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
Symbol-free definition
A subgroup of a group is termed join-transitively 2-subnormal if its join with any 2-subnormal subgroup is 2-subnormal.
Note that this is strictly stronger than the property of being 2-subnormal, because 2-subnormality is not finite-join-closed.
Formalisms
In terms of the join-transiter
This property is obtained by applying the join-transiter to the property: 2-subnormal subgroup
View other properties obtained by applying the join-transiter
Relation with other properties
Stronger properties
- Normal subgroup: For full proof, refer: Normal implies join-transitively 2-subnormal