Homology and derived series of groups

Cochran, Tim D¹ ; Harvey, Shelly L¹

¹ Department of Mathematics, Rice University, Houston, Texas 77005-1892, USA

Geometry & topology, Tome 9 (2005) no. 4, pp. 2159-2191.

Résumé

In 1964, John Stallings established an important relationship between the low-dimensional homology of a group and its lower central series. We establish a similar relationship between the low-dimensional homology of a group and its derived series. We also define a torsion-free-solvable completion of a group that is analogous to the Malcev completion, with the role of the lower central series replaced by the derived series. We prove that the torsion-free-solvable completion is invariant under rational homology equivalence.

Détail

DOI : 10.2140/gt.2005.9.2159

Keywords: derived series, group homology, Malcev completion, homological localization

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