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Invariable generation of finite classical groups

Presented by: 
Eilidh McKemmie
Date: 
Thursday 30th January 2020 - 16:05 to 16:35
Venue: 
INI Seminar Room 1
Abstract: 
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 $n \rightarrow \infty$, 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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons