A Mystery in Finite Groups of Even Order

Add 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
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 2, Newton Institute
• bld31

Note that ex-directory lists are not shown.