Images of SK₁ZG

Bruce Magurn

Vol. 79 (1978), No. 2, 531–539

DOI: 10.2140/pjm.1978.79.531

Abstract

The computation of SK₁ZG for finite nonabelian groups G remains a difficult problem. Few examples are known in which SK₁ZG is nontrivial. One way to uncover nontrivial elements is to examine the homomorphic images of SK₁ZG under K₁(−) of ring maps ZG → Λ. Such images are investigated here in the cases where Λ is a commutative ring, a noncommutative order or a semisimple artinian image of ZG. Even trivial images illuminate the structure of SK₁ZG through K-theory exact sequences.

Mathematical Subject Classification 2000

Primary: 18F25

Secondary: 16A54

Milestones

Received: 24 January 1978

Published: 1 December 1978