On Certain Distributive Lattices of Subgroups of Finite Soluble Groups

作     者：L.M.EZQUERRO X.SOLER-ESCRIV 

作者机构：InformáticaUniversidad Pública de NavarraCampus de Arrosadía.31006 PamplonaSpain Departamentde Matemàtica AplicadaUniversitat d'AlacantCampus de Sant Vicent.Ap.Correus 99-03080 AlacantSpain 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2007年第23卷第11期

页      面：2069-2078页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Proyecto BFM 2001-1667-C03-01 

主　　题：lattice properties permutability factorizations cover and avoidance properties 

摘      要：In this paper, we prove the following result. Let ξ be a saturated formation and ∑ a Hall system of a soluble group G. Let X be a w-solid set of maximal subgroups of G such that ∑ reduces into each element of X. Consider in G the following three subgroups： the ξ-normalizer D of G associated with ∑; the X-prefrattini subgroup W = W（G, X） of G; and a hypercentrally embedded subgroup T of G. Then the lattice ζ（T, W, D） generated by T, D and W is a distributive lattice of pairwise permutable subgroups of G with the cover and avoidance property. This result remains true for the lattice ,ζ（V, W, D）, where V is a subgroup of G whose Sylow subgroups are also Sylow subgroups of hypercentrally embedded subgroups of G such that ∑ reduces into V.