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UID:67286568ef1f3705af776cae1e39f208
CATEGORIES:Algebra Seminar
CREATED:20220330T105159
SUMMARY:Fixed point ratios for primitive groups and applications
LOCATION:Hill Center 425
DESCRIPTION:<p>Abstract: Let G be a finite permutation group and recall that the fixed 
 point ratio of an element x, denoted fpr(x), is the proportion of points fi
 xed by x. Fixed point ratios for finite primitive groups have been studied 
 for many decades, finding a wide range of applications. In this talk, I wil
 l present&nbsp; some of the main results and applications, focussing on rec
 ent joint work with Bob Guralnick where we determine the triples (G,x,r) su
 ch that G is primitive, x has prime order r and fpr(x) &gt; 1/(r+1). The la
 tter result allows us to prove new results on the minimal degree and minima
 l index of primitive groups, and we have used it in joint work with Moreto 
 and Navarro to study the commuting probability of p-elements in finite grou
 ps.</p>
CONTACT:Tim Burness, University of Bristol
DTSTAMP:20260827T103212
DTSTART;TZID=America/New_York:20220330T140000
DTEND;TZID=America/New_York:20220330T150000
SEQUENCE:0
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