Left-inner subgroup property: Difference between revisions
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A [[subgroup property]] <math>p</math> is said to be left-inner if, in the [[function restriction formalism]], there exists a [[restriction formal expression]] for <math>p</math> of the form: | A [[subgroup property]] <math>p</math> is said to be left-inner if, in the [[function restriction formalism]], there exists a [[restriction formal expression]] for <math>p</math> of the form: | ||
[[Inner automorphism]] <math> \to b</math> | |||
where <math>b</math> is any [[function property]]. | where <math>b</math> is any [[function property]]. | ||
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==Relation with other metaproperties== | ==Relation with other metaproperties== | ||
===Stronger metaproperties=== | |||
* [[Weaker than::Left-inner right-monoidal subgroup property]] | |||
===Weaker metaproperties=== | ===Weaker metaproperties=== | ||
* [[Left-extensibility-stable subgroup property]] | * [[stronger than::Left-extensibility-stable subgroup property]] | ||
* | * [[stronger than::intermediate subgroup condition]] | ||
Latest revision as of 21:37, 2 October 2008
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions
Definition
Symbol-free definition
A subgroup property is said to be left-inner if, in the function restriction formalism, it has a restriction formal expression with the left side being inner automorphisms.
Definition with symbols
A subgroup property is said to be left-inner if, in the function restriction formalism, there exists a restriction formal expression for of the form:
where is any function property.
In other words, a subgroup satisfies property in if and only if every inner automorphism on restricts to a function on the subgroup satisfying property .
In terms of the left expressibility operator
The subgroup metaproperty of being left-inner is obtained by applying the left expressibility operator to the function metaproperty of being exactly equal to the inner automorphism