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On Representing Finite Lattices as Intervals in Subgroup Lattices of Finite Groups

✍ Scribed by Robert Baddeley; Andrea Lucchini

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
832 KB
Volume
196
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let M M be the lattice of length 2 with n G 1 atoms. It is an open problem to n Ε½ decide whether or not every such lattice or indeed whether or not every finite . lattice can be represented as an interval in the subgroup lattice of some finite group. We complete the work of the second author, Lucchini, by reducing this problem to a series of questions concerning the finite non-abelian simple groups.

πŸ“œ SIMILAR VOLUMES

On Lattices of p β€”Local Formations of Fi
On Lattices of p β€”Local Formations of Finite Groups
✍ A. Ballester-Bolinches; L. A. Shemetkov πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 500 KB

Throughout the paper we consider only finite groups. In [l] W. GASCHUTZ introduced the notion of formation which is useful and convenient for stu.dying not only groups but also other algebraic systems (see [2]). Recall that a class 3 of groups is called a formation if it is closed under taking homo