A normal subgroup theorem for commensurators of lattices

Pseudocomplementation in (normal) subgroup lattices

The goal of this paper is to study finite groups admitting a pseudocomplemented subgroup lattice (PK-groups) or a pseudocomplemented normal subgroup lattice (PKN-groups). In particular, we obtain a complete classification of finite PK-groups and of finite nilpotent PKN-groups. We also study groups with a Stone normal subgroup lattice, and we classify finite groups for which every subgroup has a...

Complementation in normal subgroup lattices

The goal of this survey is to study some classes of groups determined by different types of complementation of their normal subgroup lattices. The groups whose normal subgroup lattices are Stone lattices, boolean lattices or ortholattices will be also investigated. MSC (2000): Primary 20D30, Secondary 20E15, 06C15, 06D15.

Margulis’s normal subgroup theorem A short introduction

The normal subgroup theorem of Margulis expresses that many lattices in semi-simple Lie groups are simple up to finite error. In this talk, we give a short introduction to the normal subgroup theorem , including a brief review of the relevant notions about lattices, amenability, and property (T), as well as a short overview of the proof of the normal subgroup theorem. 1 Margulis's normal subgro...

Commutativity Criterions Using Normal Subgroup Lattices

We prove that a group G is Abelian whenever (1) it is nilpotent and the lattice of normal subgroups of G is isomorphic to the subgroup lattice of an Abelian group or (2) there exists a non-torsion Abelian group B such that the normal subgroup lattice of B × G is isomorphic to the subgroup lattice of an Abelian group. Using (2), it is proved that an Abelian group A can be determined in the class...

Rigidity of Commensurators and Irreducible Lattices