TY - JOUR
AU - Gardener, T. S.
AB - T. S. GARDENER 1. Introduction In his paper Les automorphisms d'un ensemble fortement minimal [4] Lascar develops methods of finding normal subgroups of automorphism groups of countable saturated structures. These methods are very well suited, for example, to the symmetric group on an infinite countable set and so provide a new proof of the result of Schreier and Ulam [7] that the quotient of the symmetric group by the finitary subgroup is simple. A further application is to countably infinite vector spaces over countable fields. Again it turns out that the quotient of the automorphism group by, in some sense, a 'finitary' subgroup is simple. This was already proved in much greater generality by Rosenberg in [6]. Results of this type are known for some X - categorical theories which are not stable. We adapt Lascar's methods to vector spaces over finite fields of countable dimension equipped with symplectic, unitary or orthogonal forms. We prove the main result in the case where Fis a symplectic space over a finite field and later we outline the amendments necessary to deal with the unitary and orthogonal cases. We also note that in the symplectic case the requirement that the field be 
TI - Infinite Dimensional Classical Groups
JO - Journal of the London Mathematical Society
DO - 10.1112/jlms/51.2.219
DA - 1995-04-01
UR - https://www.deepdyve.com/lp/wiley/infinite-dimensional-classical-groups-VHm7UNyFOU
SP - 219
EP - 229
VL - 51
IS - 2
DP - DeepDyve
ER -