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SUMMARY:Generation of finite simple groups  - Carlisle King\, Imperial Col
 lege
DTSTART:20160212T150000Z
DTEND:20160212T160000Z
UID:TALK64130@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:Given a finite simple group G\, it is natural to ask how many 
 elements are needed to generate G. It has been shown that all finite simpl
 e groups are generated by a pair elements. A natural refinement is then to
  ask whether the orders of the generating elements may be restricted: give
 n a pair of integers (a\,b)\, does there exist a pair of elements (x\,y) g
 enerating G with x of order a and y of order b? If such a pair exists\, we
  say G is (a\,b)-generated. I will explore some past results regarding (2\
 ,3)-generation as well as a new result on (2\,p)-generation for some prime
  p.
LOCATION:CMS\, MR4
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