Local indicability and relative presentations of groups

✍ Scribed by Julia D. Fredericks

• Book ID: 104152570
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 150 KB
• Volume: 177
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(02)00144-5

✦ Synopsis

A relative presentation is a triple P = (A; X : R) where A is a group, X is a set, and R is a set of words in the free product A * F(X ) where F(X ) is the free group with basis X . Under certain hypotheses on the relative presentation P, we show that (1) the group presented by P is locally indicable; (2) the pre-aspherical model for P is aspherical; (3) the Freiheitssatz holds for P. The result has applications in the computation of cohomology of groups and the ÿeld of equations over groups.