Structure of definable linear groups in a field of finite Morley rank

[摘要] We generalize several properties of linear algebraic groups to the case of the linear groups which are defined in a field of finite Morley rank. We show three structure theorems and the conjugacy of the borels, of the Carter subgroups, of the maximal tori. In conclusion we generalize the results to fields of Morley rank omega.n without subgroups of finite rank. In contrary to the case of finite Morley rank there are known examples of such fields with definable non-algebraic subgroups of GL(n)(K). (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-11-15