Measuring the associativity of loops

Abstract: In group theory folklore, there is a well-known theorem; The probability that two randomly uniformly chosen elements commute in a non-abelian group $G$ cannot exceed 5/8. The bound is attained by the Quaternion group $Q_8$. In this talk, we shall discuss a non-associative analog of the theorem. Namely, the probability of three randomly chosen elements associating is bounded by 43/64 in Moufang loops with nuclear commutators, with the bound attained by the Octonion loop $O_{16}$.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar