- Serre's property FA
Property FA is a property of mathematical groups.
Jean-Pierre Serredefined property FA in his book "Arbres, amalgames, " (published in English, translated by John Stilwell, as "Trees").
A group "G" is said to have property FA if every action of "G" on a tree has a global
Serre shows in "Trees" that if a group has property FA, then it cannot split as a free product with amalgamation or
HNN extension. In particular, a finitely generated group with property FA has finite abelianization.
It is a theorem of Watatani that Kazhdan's property (T) implies property FA of Serre.
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