The Non-abelian Specker-Group Is Free

The paper investigates a group H which can be constructed as a subgroup of the inverse limit of the finitely generated free groups Fn by taking only those elements , for which there exists some bound b(g) such that none of the generators of any of the groups Fn occurs more often than b(g) times in any of the entries of at least one sequence of Fn-elements describing g. By using a similar condition, H can also be described as a subgroup of the fundamental group of the Hawaiian Earrings. Despite not having any obvious candidate for a free basis, H is proven to be free by a non-constructive basis selection method. Since H is related to the same way as the classical Specker group is related to , we decided to call H the “non-abelian Specker group.”