Invariable generation of finite classical groups

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• Eilidh McKemmie, University of Southern California
• Thursday 05 March 2020, 16:00-17:00
• Lecture Theatre B, Watson Building.

If you have a question about this talk, please contact Simon Goodwin.

We say a group is invariably generated by a subset if it forms a generating set even if an adversary is allowed to replace any elements with their conjugates. Eberhard, Ford and Green built upon the work of many others and showed that, as n tends to infinity, the probability that S_n is invariably generated by a random set of elements is bounded away from zero if there are four random elements, but goes to zero if we pick three random elements. This result gives rise to a nice Monte Carlo algorithm for computing Galois groups of polynomials. We will extend this result for S_n to the finite classical groups using the correspondence between classes of maximal tori of classical groups and conjugacy classes of their Weyl groups.

This talk is part of the Algebra seminar series.

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• Algebra seminar
• Lecture Theatre B, Watson Building
• School of Mathematics events

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