Physical Sciences and Mathematics Commons^™

Algorithms For Upper Bounds Of Low Dimensional Group Homology, Joshua D. Roberts

University of Kentucky Doctoral Dissertations

A motivational problem for group homology is a conjecture of Quillen that states, as reformulated by Anton, that the second homology of the general linear group over R = Z[1/p; ζ_p], for p an odd prime, is isomorphic to the second homology of the group of units of R, where the homology calculations are over the field of order p. By considering the group extension spectral sequence applied to the short exact sequence 1 → SL₂ → GL₂ → GL₁ → 1 we show that the calculation of the homology …