On Simple K4-Groups

On Weyl Groups in Minimal Simple Groups of Finite

We prove that generous non-nilpotent Borel subgroups of connected minimal simple groups of finite Morley rank are self-normalizing. We use this to introduce a uniform approach to the analysis of connected minimal simple groups of finite Morley rank through a case division incorporating four mutually exclusive classes of groups. We use these to analyze Carter subgroups and Weyl groups in connect...

On the Representation of Simple Riesz Groups

In this paper we answer Open Problem 2 of Goodearl’s book on partially ordered abelian groups in the case of partially ordered simple groups. As a consequence, we obtain a version of the Theorem of structure of dimension groups in the case of simple Riesz groups. Also, we give a method for constructing torsion-free strictly perforated simple Riesz groups of rank one, and we see that every dense...

On Simple Groups of Finite Order. I

On finite simple groups and Kneser graphs

For a finite group G let (G) be the (simple) graph defined on the elements of G with an edge between two (distinct) vertices if and only if they generate G. The chromatic number of (G) is considered for various non-solvable groups G.

On Multicommutators for Simple Algebraic Groups

There are several examples of groups for which any pair of commutators can be written such that both of them have a common entry, and one can look for a similar property for n-tuples of commutators. We here answer, for simple algebraic groups over any field, the weaker question, under which condition the set of n-tuples of commutators with one common entry is Zariski dense in the set of all n-t...