Generation of integral orthogonal groups over dyadic local fields

Fei Xu

Vol. 167 (1995), No. 2, 385–398

DOI: 10.2140/pjm.1995.167.385

Abstract

In this paper, we introduce the minimal norm Jordan splittings of quadratic lattices over dyadic local fields. By using these splittings, we prove that orthogonal groups over dyadic local fields are generated by the symmetries and the Eichler transformations of the lattices unless the spinor norms of these groups are entire multiplicative groups of underlying fields.

Mathematical Subject Classification 2000

Primary: 11E08

Secondary: 11E57, 20G25

Milestones

Received: 10 July 1992

Published: 1 February 1995