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SUMMARY:Generating finite classical groups by elements with large fixed po
 int spaces - Cheryl Praeger\, University of Western Australia
DTSTART:20140312T163000Z
DTEND:20140312T173000Z
UID:TALK50368@talks.cam.ac.uk
CONTACT:David Stewart
DESCRIPTION:Constructing standard generators for finite classical groups i
 n even characteristic\nseemed much more difficult than the same problem in
  odd characteristic\,\nwhere ingenious methods using involution centralise
 rs were available. Innovative new\nprocedures developed by Neunhoeffer and
  Seress\, and by Dietrich\, Leedham-Green\, \nLubeck and O'Brien seem to h
 ave solved the problem: justifying these new methods\nrequires proof that 
 the groups can be generated efficiently by elements with large fixed point
  spaces.  \n\nI will talk about a problem which lies at the heart of analy
 sis:  determine the\nprobability of generating a finite 2n-dimensional cla
 ssical group by two random conjugates \nof a `good element' t\, namely |t|
  is divisible by a primitive prime divisor of q^n-1 \nfor the relevant fie
 ld order q\, and t fixes pointwise an n-space. The problem had some \nstra
 nge "twists and turns".
LOCATION:MR12
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