Mathematics Colloquium: Geometry of involutions and black box algebra

- FENS
- Mathematics Colloquium: Geometry of involutions and black box algebra

In this talk, I will discuss characterizations of the groups PSL2 and PSL3 over fields of odd characteristic via geometry of involutions (elements of order 2) in the context of black box groups. Starting with the black box groups encrypting PSL2 and PSL3, I will discuss a construction of the black box projective plane and its coordinatization which will yield a solution to a recognition problem for these groups.

I will also discuss a solution of a twenty year old problem in the computational group theory, that is, a construction of a unipotent element in a black box group encrypting PSL2.

This is a joint work with Alexandre Borovik.

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