Second cohomology groups and finite covers of infinite symmetric groups

JOURNAL OF ALGEBRA

卷:330

Article

Evans, David M.²  Pastori, Elisabetta¹ 

[1] Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy

[2] Univ E Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England

关键词: Infinite permutation groups;    Continuous cohomology groups;    Permutation modules for the symmetric;    group of infinite degree;    Finite covers in model theory;   

DOI  :  10.1016/j.jalgebra.2010.12.004

来源: Elsevier

【 摘 要 】

For Omega an infinite set, k >= 2 and W the set of k-sets from Omega, there is a natural closed permutation group Gamma(k) which is a non-split extension 0 -> Z(2)(W) -> Gamma(k) -> Sym(Omega) -> 1. We classify the closed subgroups of Gamma(k) which project onto Sym(Omega). The question arises in model theory as a problem about finite covers, but here we formulate and solve it in algebraic terms. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free