We present explicit upper bounds for the number and size of conjugacy classes in finite Chevalley groups and their variations. These results have been used by many authors to study zeta functions associated to representations of finite simple groups, random walks on Chevalley groups, the final solution to the Ore conjecture about commutators in finite simple groups and other similar problems. I...

The aim of this note is to classify all weakly closed unipotent subgroups in the split Chevalley groups. In an application we show under some mild assumptions on the characteristic that 2 dimX + dim cg(X) < dim g for X a non-trivial unipotent subgroup of the connected simple algebraic group G. This shows the failure of the analogue of the so called “2F-condition” for finite groups for the adjoi...

We show that the Sylow 2-subgroups of nearly all Chevalley groups in even characteristic allow the definition of a check-character-system which detects all single and the most important double errors.

On the basis of the Bruhat decomposition, the subgroups generated by pairs of unipotent short root subgroups in Chevalley groups of type B , C , and F4 over an arbitrary field are described. Moreover, the orbits of a Chevalley group acting by conjugation on such pairs are classified.

Let M∗(q) be the unique nonassociative finite simple Moufang loop constructed over GF (q). We prove that Aut(M∗(2)) is the Chevalley group G2(2), by extending multiplicative automorphism of M∗(2) into linear automorphisms of the unique split octonion algebra over GF (2). Many of our auxiliary results apply in the general case. In the course of the proof we show that every element of a split oct...

The classical Waring problem deals with expressing every natural number as a sum of g(k) k powers. Similar problems were recently studied in group theory, where we aim to present group elements as short products of values of a given word w 6= 1. In this paper we study this problem for Lie groups and Chevalley groups over infinite fields. We show that for a fixed word w 6= 1 and for a classical ...