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Classical groups, and generating small classical subgroups

Presented by: 
Cheryl Praeger
Friday 31st January 2020 - 13:45 to 14:35
INI Seminar Room 1
I will report on on-going work with Alice Niemeyer and Stephen Glasby. In trying to develop for finite classical groups, some ideas Akos Seress had told us about special linear groups, we were faced with the question:

"Given two non-degenerate subspaces U and W, of dimensions e and f respectively, in a formed space of dimension at least e+f, how likely is it that U+W is a non-degenerate subspace of dimension e+f?"

Something akin to this question, in a similar context is addressed in Section 5 of "Constructive recognition of classical groups in even characteristic" (J. Algebra 391 (2013), 227-255, by Heiko Dietrich, C.R.Leedham-Green, Frank Lubeck, and E. A. O’Brien). We wanted explicit bounds for this probability, and then to apply it to generate small classical subgroups.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons