Generating finite classical groups by elements with large fixed point spaces

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• Cheryl Praeger, University of Western Australia
• Wednesday 12 March 2014, 16:30-17:30
• MR12.

If you have a question about this talk, please contact David Stewart.

Constructing standard generators for finite classical groups in even characteristic seemed much more difficult than the same problem in odd characteristic, where ingenious methods using involution centralisers were available. Innovative new procedures developed by Neunhoeffer and Seress, and by Dietrich, Leedham-Green, Lubeck and O’Brien seem to have solved the problem: justifying these new methods requires proof that the groups can be generated efficiently by elements with large fixed point spaces.

I will talk about a problem which lies at the heart of analysis: determine the probability of generating a finite 2n-dimensional classical group by two random conjugates of a `good element’ t, namely |t| is divisible by a primitive prime divisor of q^n-1 for the relevant field order q, and t fixes pointwise an n-space. The problem had some strange “twists and turns”.

This talk is part of the Algebra and Representation Theory Seminar series.

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