John R. Britnell (Bristol, UK):
   The probability that two elements of a finite group are conjugate

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Abstract:
The probability that two elements chosen independently at random from a
finite group G are conjugate is a statistic which has received
surprisingly little attention. I shall discuss some general observations
about this probability, and indicate how to classify groups for which it 
is
at least 1/4. I shall also describe some asymptotic results for symmetric
groups.