[Back]

W. Herfort, W. Hojka:
"Cotorsion and Wild Homology";
Israel Journal of Mathematics (invited), 221 (2017), 275 - 290.

The classical concept of cotorsion of an abelian group is here characterized in the style of algebraic compactness, namely by the existence of solutions of certain systems of equations. This approach further highlights the close relation between the two concepts. Then the natural extension to nonabelian groups is related to a topological property and used to determine the first singular homology group of wild spaces.
As a further application, it is shown that the abelianization of the quotient *_i G_i / ( \bigfree_i G_i) is isomorphic to \prod_i \Z / \bigoplus_i \Z, for arbitrary nontrivial groups $G_i$ of cardinality at most the continuum.

Kotorsion abelscher Gruppen laesst sich mittels spezieller unendlcher Gleichungssystem, besser deren Loesbarkeit, charakterisieren. Da, wie in der Arbeit gezeigt wird, sog. small loop Raeume eine Higman vollstaendige Fundamentalgruppe haben, und diese im Abelschen Fall genau Kotorsion bedeutet, kann die Struktur der 1.ten Homologiegruppe von sog. Archipel-Raeumen konkret beschrieben werden.

wild space, archipelago group, HIgman completeness, cotorsion

http://dx.doi.org/10.1007/s11856-017-1566-z