Solvability and nilpotence just beyond groups

Abstract: Solvability and nilpotence arise naturally from the commutator theory in congruence modular varieties. In the presence of associativity, the resulting concepts agree with the classical concepts of group theory. But the two kinds of solvability differ in loops ( = not necessarily associative groups) and it is a difficult question to determine the boundary where the two theories coincide. I will review the general theory and report on recent results, particularly in Moufang loops. For instance, we will prove the Odd Order Theorem for Moufang loops for the stronger notion of solvability. This is joint work with Ales Drapal and David Stanovsky.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar