Resumen de Spaces associated to quadratic endofunctors of the category of groups

Hans-Joachim Baues, Teimuraz Pirashvili

• Square groups are gadgets classifying quadratic endofunctors of the category of groups. Applying such a functor to the Kan simplicial loop group of the 2-dimensional sphere one obtains a one-connected three-type. We consider the problem of characterization of those three-types X which can be obtained in this way. We solve this problem in some cases, including the case when ¿2(X) is a finitely generated abelian group. The corresponding stable problem is solved completely.