Regular elements in CAT(0) groups

Regular Elements of Finite Reflection Groups

Regular Elements in Algebraic Groups of Prime Characteristic

A result of Steinberg's on the existence of rational regular unipotent elements in quasi-split simple algebraic groups over fields of arbitrary characteristic is partially extended to the case of non-quasi-split groups.

Regular Elements and Monodromy of Discriminants of Finite Reflection Groups

where the product is over all reflection hyperplanes of G. Let A : V/G -+ @ be the map induced by 6, thus A is the discriminant of G. A subgroup of G is called parabolic if it is generated by all reflections of G fixing elementwise a given subspace of V. The degrees of G are denoted by dl , d2, . . . , d,,. We call a degree of G primitive if it is bigger than the degrees of all proper parabolic...

Pairwise‎ ‎non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

Cohomology of Deligne-Lusztig varieties for short-length regular elements in exceptional groups

We determine the cohomology of Deligne-Lusztig varieties associated to some short-length regular elements for split groups of type F4 and En. As a byproduct, we obtain conjectural Brauer trees for the principal Φ14-block of E7 and the principal Φ24-block of E8.