turkmath.org

Over the last few decades, there has been a major interest in computational group theory to produce efficient recognition algorithms for matrix groups over finite fields. In this talk, I will focus on the black box set up, that is, the groups are encrypted in 0-1 strings of uniform length, and group operations, taking inverses and comparing elements for equality are performed by a black box. I will discuss the fundamental difficulties in matrix groups and present a uniform approach for an efficient recognition of finite groups of Lie type of odd characteristic. I will also discuss a solution of a long standing open problem of constructing a unipotent element in black box groups of Lie type. This is a joint work with Alexandre Borovik.