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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > A Mystery in Finite Groups of Even Order

## A Mystery in Finite Groups of Even OrderAdd to your list(s) Download to your calendar using vCal - George Glauberman (University of Chicago; University of Chicago)
- Thursday 16 January 2020, 16:00-17:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact INI IT. GRA - Groups, representations and applications: new perspectives Often in mathematics, we have a reason for believing that something is true, but not a proof. I plan to discuss a result that has 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. An easy proof shows that xy has even order. Now take an element u that lies in a normal subgroup of odd order in the centralizer of x in G, and an analogous element v for y. Then (xu)(yv) also has even order. This result was obtained by simple-minded manipulation of group characters, rather than by theory or intuition about the structure of a finite group. Suggestions for reasons are welcome. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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