A classification of fully residually free groups of rank three or less
A group \(G\) is said to be fully residually free provided to every finite set \(S\) consisting of nontrivial elements there are a free group \(F\) and an homomorphism \(\varphi\colon G\to F\) such that every image \(\varphi(s)\), \(s\in S\) is nontrivial too. This property has been of great interest recently in terms of the study of questions in logic pertaining to certain other freeness properties in groups, and in connection with free tree actions. A group \(G\) is called \(n\)-free provided every subgroup of \(G\) generated by \(n\) elements is free. It is shown in the paper that every \(2\)-free residually free group is \(3\)-free. There are \(3\)-free fully residually free groups which are not \(4\)-free.
scientific article; zbMATH DE number 1139791
scientific article