Simplicity of some automorphism groups

JOURNAL OF ALGEBRA

卷:342

Article

Macpherson, Dugald²  Tent, Katrin¹ 

[1] Univ Munster, Math Inst, D-48149 Munster, Germany

[2] Univ Leeds, Dept Pure Math, Leeds LS2 9JT, W Yorkshire, England

关键词: Simple groups;    Automorphism groups;    Polish groups;    Fraisse limits;   

DOI  :  10.1016/j.jalgebra.2011.05.021

来源: Elsevier

【 摘 要 】

Let M be a countably infinite first order relational structure which is homogeneous in the sense of Fraisse. We show, under the assumption that the class of finite substructures of M has the free amalgamation property, along with the assumption that Aut(M) is transitive on M but not equal to Sym(M), that Aut(M) is a simple group. This generalises results of Truss, Rubin and others. The proof uses the Polish group structure of the automorphism group and generalises to certain other homogeneous structures, with prospects for further application. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free