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SUMMARY:Cycles in Permutation Groups - Cheryl Praeger (University of Weste
 rn Australia)
DTSTART:20220616T150000Z
DTEND:20220616T160000Z
UID:TALK175301@talks.cam.ac.uk
DESCRIPTION:The question which I hope to address in this lecture is: Why c
 are about cycles in permutation groups?&nbsp\; It has engaged mathematicia
 ns for around 150 years\, going back to Jordan&rsquo\;s seminal result tha
 t the finite primitive permutation groups containing a prime length cycle 
 with at least three fixed points are the giants\, the alternating group an
 d symmetric group. From the 1970&rsquo\;s\, this and other old results off
 ered a means of identifying these giants among primitive groups computatio
 nally\, using random selections to find such elements. The computational a
 pplication raised a further question: Just how easy is it to find\, or con
 struct\, one of these Jordan cycles? &nbsp\;I&rsquo\;ll trace this story u
 p to 2021\, when with Stephen Glasby and Bill Unger we found a (to us surp
 rising) answer.&nbsp\; &nbsp\;If there is time I'll draw a parallel with s
 tingray matrices in finite classical groups.
LOCATION:Seminar Room 2\, Newton Institute
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