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SUMMARY:Adam Chapman (Academic College of Tel-Aviv-Yaffo\, Israel)
DTSTART:20260302T150000Z
DTEND:20260302T160000Z
DTSTAMP:20260423T021156Z
UID:ENAAS/163
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/163/">
 Measuring the associativity of loops</a>\nby Adam Chapman (Academic Colleg
 e of Tel-Aviv-Yaffo\, Israel) as part of European Non-Associative Algebra 
 Seminar\n\n\nAbstract\nIn group theory folklore\, there is a well-known th
 eorem\; The probability that two randomly uniformly chosen elements commut
 e in a non-abelian group $G$ cannot exceed 5/8. The bound is attained by t
 he Quaternion group $Q_8$. In this talk\, we shall discuss a non-associati
 ve analog of the theorem. Namely\, the probability of three randomly chose
 n elements associating is bounded by 43/64 in Moufang loops with nuclear c
 ommutators\, with the bound attained by the Octonion loop $O_{16}$.\n
LOCATION:https://researchseminars.org/talk/ENAAS/163/
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