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Loops de Moufang Loops and related groups

Grant number: 17/14489-2
Support type:Research Grants - Visiting Researcher Grant - International
Duration: October 15, 2017 - April 14, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Alexandre Grichkov
Grantee:Alexandre Grichkov
Visiting researcher: Andrei Zavarnitsine
Visiting researcher institution: Siberian Branch of the Russian Academy of Sciences (SB RAS), Russia
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:14/09310-5 - Algebraic structures and their representations, AP.TEM

Abstract

By definition a loop M is a Moufang loop if it satisfies an identity (xy)(zx)=(x(yz))x.The Project is dedicate to study of (finite) Moufang loops and its connnection with group with triality.In particular, we plan to work over the following problems:1. Let L be a finite Moufang p-loop L with p >3 be generated by a set X. If (x; y; z) =1 for all x; y; z from X. Then does it imply that L is associative?2. Let M be a Moufang loop and G be the corresponding (minimal) group withtrialty.What means in the term of G the fact: the loop M is isomorphic to all its isotops?3.We describe yet the extentions of Moufang loops with cyclic groups of order prime with 6. We plan to extend this result for other cyclic groups.For solve those problem it is importent to prove (in positive sense) the following problem:Is it true that every pseudoautomorphism of a Moufang loop is the product ofan inner pseudoautomorphism and an automorphism? (AU)