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University of Sydney Algebra Seminar

Don Taylor

Friday 4 November, 2-3pm, Place: Carslaw 451

Matrix group recognition and finite groups of Lie type

Constructive recognition algorithms are an important part of the 'matrix group recognition project', the aim of which is to enable effective computation in matrix groups over finite fields. Probabilistic algorithms reduce the problem to finding a constructive isomorphism between a quasisimple group and a `standard copy'. Suppose H is a matrix group known to be a finite group of Lie type and let G be a reductive group with a homomorphism from G onto H. If A is a matrix in H, an essential part of the recognition process is to write an inverse image of A as a word in the Steinberg generators of G. In this talk I will give an outline of an algorithm for simply connected finite groups of Lie type, including the twisted groups.