The Group Properties Wiki (pre-alpha)
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Function property
From Groupprops
This article is about a general term. A list of important particular cases (instances) is available at Category:Function properties
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Definition
A function property is a map from the collection of all possible functions from a group to itself, to the two-element set (true, false). A function which gets mapped to true is said to have the function property, and a function which gets mapped to false is said to not have the function property.
The function property must satisfy isomorphism-invariance: if 
and 
are functions, and there is an isomorphism 
such that 
, then f1 satisfies the function property iff f2 satisfies the function property.
