SEMINAR: Groups and Combinatorics Seminar, The Wall and Guralnick conjectures: history and legacy
|Groups and Combinatorics Seminar, The Wall and Guralnick conjectures: history and legacy
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.
- Locations of venues on the Crawley and Nedlands campuses are
available via the Campus Maps website.
- Download this event as:
Mail this event: