Vasil’ev, A. F.; Kamornikov, S. F. On the functorial method for studying the lattices of subgroups of finite groups. (Russian, English) Zbl 0983.20018 Sib. Mat. Zh. 42, No. 1, 30-40 (2001); translation in Sib. Math. J. 42, No. 1, 25-33 (2001). A functorial approach is proposed for generalizing H. Wielandt’s result [Math. Z. 45, 209-244 (1939; Zbl 0021.21003)] that all subnormal subgroups of a group form a lattice. Axiomatizing the main properties of subnormal subgroups (invariance under homomorphisms, transitivity, heredity in subgroups), the authors introduce the notion of natural, transitive, lattice functor and describe all lattices induced by such functors in finite solvable groups. As a consequence, the hereditary formations with the lattice property in the universe of all finite solvable groups are described. Some open problems are formulated. Reviewer: A.V.Zavarnitsine (Novosibirsk) Cited in 6 Documents MSC: 20D30 Series and lattices of subgroups 20D35 Subnormal subgroups of abstract finite groups 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks Keywords:subnormal subgroups; lattices of subgroups; lattice functors; hereditary formations; finite solvable groups Citations:Zbl 0021.21003 PDFBibTeX XMLCite \textit{A. F. Vasil'ev} and \textit{S. F. Kamornikov}, Sib. Mat. Zh. 42, No. 1, 30--40 (2001; Zbl 0983.20018); translation in Sib. Math. J. 42, No. 1, 25--33 (2001) Full Text: EuDML