Large element orders and the characteristic of Lie-type simple groups

Large element orders and the characteristic of Lie-type simple groups

Given a matrix group G = 〈X〉 GL(d,q), specified by a set X of generators, it seems that a full structural exploration of G is necessary in order to answer even the simplest questions concerning G , such as finding |G| or testing the membership of any given matrix in G (cf. [LG,BB]). Currently, the standard approach to such an exploration is to set up a recursive scheme of homomorphisms, breakin...

Black-box recognition of finite simple groups of Lie type by statistics of element orders

Given a black-box group G isomorphic to some finite simple group of Lie type and the characteristic of G, we compute the standard name of G by a Monte Carlo algorithm. The running time is polynomial in the input length and in the time requirement for the group operations in G. The algorithm chooses a relatively small number of (nearly) uniformly distributed random elements of G, and examines th...

the investigation of the relationship between type a and type b personalities and quality of translation

چکیده ندارد.

Counting lattices in simple Lie groups: the positive characteristic case

In this article we prove a conjecture of A. Lubotzky: let G = G0(K), where K is a local field of characteristic p ≥ 5, G0 is a simply connected, absolutely almost simple K-group of K-rank at least 2. We give the rate of growth of ρx(G) := |{Γ ⊆ G|Γ a lattice in G, vol(G/Γ) ≤ x}/ ∼ |, where Γ1 ∼ Γ2 if and only if there is an abstract automorphism θ of G such that Γ2 = θ(Γ1). We also study the ra...

Topology of Lie Groups and Characteristic Classes