Characterization of classical groups by orbit sizes on the natural module

We show that if is a finite vector space, and is a subgroup of having the same orbit sizes on 1-spaces as an orthogonal or unitary group on , then, with a few exceptions, is itself an orthogonal or unitary group on .

     

The length and depth of algebraic groups

Mathematische Zeitschrift - Let G be a connected algebraic group. An unrefinable chain of G is a chain of subgroups $$G = G_0> G_1> \cdots > G_t = 1$$ , where each $$G_i$$ is a...     

Factorizations of simple algebraic groups

We determine all factorizations of simple algebraic groups as the product of two maximal closed connected subgroups. Additional results are established which drop the maximality assumption, and applications are given to the study of subgroups of classical groups transitive on subspaces of a given dimension.

     

The probability of generating a finite simple group

We show that two random elements of a finite simple groupG generateG with probability 1 as |G| . This settles a conjecture of Dixon.     

Finding the characteristic of a group of Lie type

We present a black-box polynomial-time Monte Carlo algorithmwhich, given as input a quasi-simple group of Lie type, findsits characteristic.