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Transfer condition
From Groupprops
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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
This article is about a general term. A list of important particular cases (instances) is available at Category:Subgroup properties satisfying transfer condition
Definition
Definition with symbols
A subgroup property p is said to satisfy the transfer condition if whenever H satisfies property p as a subgroup of G, and K is a subgroup of G, then H ∩ K satisfies property p as a subgroup of K.
Formalisms
Consider the procedure P that takes as input a group-subgroup pair 
, and outputs all group-subgroup pairs 
for 
. The transfer condition is the single-input-expressible metaproperty corresponding to procedure P: a subgroup property p satisfies the transfer condition if satisfying property p implies that all pairs also satisfy property p.
Relation with other metaproperties
Stronger metaproperties
Weaker metaproperties
Conjunction implications
- Any transitive subgroup property that satisfies the transfer condition is also finite-intersection-closed. For full proof, refer: Transitive and transfer condition implies finite-intersection-closed
Metametaproperties
Conjunction-closedness
This subgroup metaproperty is conjunction-closed: an arbitrary conjunction (AND) of subgroup properties satisfying this metaproperty, also satisfies this metaproperty
View conjunction-closed subgroup metaproperties
Disjunction-closedness
This subgroup metaproperty is disjunction-closed: an arbitrary disjunction (OR) of subgroup properties satisfying this metaproperty, also satisfies this metaproperty
View all disjunction-closed subgroup metaproperties
Composition-closedness
This subgroup metaproperty is composition-closed: the property obtained by applying the composition operator to two subgroup properties satisfying this metaproperty, also satisfies this metaproperty
View a complete list of composition-closed subgroup metaproperties
Facts about Transfer conditionRDF feed
