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SUMMARY:A Mystery in Finite Groups of Even Order - George Glauberman (Univ
 ersity of Chicago\; University of Chicago)
DTSTART:20200116T160000Z
DTEND:20200116T170000Z
UID:TALK136753@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Often in mathematics\, we have a reason for believing that som
 ething is true\, but not a proof.&nbsp\; I plan to discuss a result that h
 as a proof\, but no clear reason.  Let x and y be elements of order two in
  a finite group G that are not conjugate in G.&nbsp\; An easy proof shows 
 that xy has even order.&nbsp\; Now take an element u that lies in a normal
  subgroup of odd order in the centralizer&nbsp\; of x in G\, and an analog
 ous element v for y.&nbsp\; Then (xu)(yv)  also has even order.&nbsp\;&nbs
 p\; This result was obtained by simple-minded  manipulation of group chara
 cters\, rather than by theory or intuition about the structure of a finite
  group.&nbsp\; Suggestions for reasons are welcome.  <br><br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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