Local-global principle for congruence subgroups of Chevalley groups

Intermediate Subgroups in Chevalley Groups

Let G be a group and D be a subgroup of G. In this paper we are interested in the description of the lattice L(D; G) = fH j D H Gg of subgroups of G which contain D. We call subgroups H 2 L(D; G) subgroups intermediate between D and G. We are primarily interested in the parametrization of intermediate subgroups and their behaviour with respect to set-theoretic and group-theoretic operations lik...

Weakly Closed Unipotent Subgroups in Chevalley Groups

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...

Congruence Subgroups of Groups Commensurable with PSL

One-Cusped Congruence Subgroups of Bianchi Groups

We show that there are only finitely many maximal congruence subgroups of the Bianchi groups such that the quotient by H has only one cusp.

Generation of Pairs of Short Root Subgroups in Chevalley Groups

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.