SEMINAR:
Groups and Combinatorics Seminar, The Wall and Guralnick conjectures: history and legacy
Fri, 01 Mar 2013 15:00 - MLR2
Leonard Scott
Abstract:
In 1961 G.E. Wall conjectured that the number of maximal subgroups of a
finite group is less than the order of the group. The conjecture holds
for all finite solvable groups (proved by Wall himself in his original
paper) and holds for almost all finite simple groups, possibly all of
them (proved by Liebeck, Pyber and Shalev in 2007). It is now known to
be false in general, at least as originally stated, with infinitely many
negative composite group examples found through a combination of
computational and theoretical techniques. (I cite in particular computer
calculations of Frank Luebeck, as partly inspired and later confirmed by
calculations of my undergraduate student, Tim Sprowl, with theoretical
input from myself and Bob Guralnick.) In this talk I will try to
discuss the ingredients in this quite remarkable story, and I will
mention as much of the legacy of positive consequences as time permits.
For more information:
Irene Pivotto
irene.pivotto@uwa.edu.au
Starts : Fri, 01 Mar 2013 15:00
Ends : Fri, 01 Mar 2013 16:00
Last Updated : Fri, 01 Mar 2013 11:36