Loops and related groups

• Grant number: 21/13052-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2022
• End date: July 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Alexandre Grichkov
• Grantee: Luis Augusto de Mendonça
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/23690-6 - Structures, representations, and applications of algebraic systems, AP.TEM

Abstract

Automorphic loops. Let L be a loop and G the multiplication group of loop L, generated by left and right multiplication operators. We denote H(L) = StabG(L)(e), where ex = xe = x. The loop L is called automorph if H(L) is in Aut(L). There are few explicit constructions of automorph loops. The problem of calculating H(L) groupsand Aut(L) are still open.We emphasize that this problem is related to the problem of calculating Aut(P), where P is a metabelian Lie algebra. Mixed Steiner systems and related quasigroups. Let P be a set and L(P) a system of subsets of P. In this case L(P) ifcalls Steiner's system if for any s of L(P) we have |s| = n and for some m

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

KLOPSCH, BENJAMIN; MENDONCA, LUIS; PETSCHICK, JAN MORITZ. Free polynilpotent groups and the Magnus property. FORUM MATHEMATICUM, v. N/A, p. 18-pg., 2023-01-30. (21/13052-5)