Commutative automorphic loops nilpotent of degree three

• Grant number: 10/16112-4
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2011
• End date: February 28, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Alexandre Grichkov
• Grantee: Dylene Agda Souza de Barros
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Our goal is to study the A-loops commutative nilpotent of degree 3 for the classification of commutative A-loops of order p4, where p is a prime number.We already have the classification of commutative A-loops of order p3 and such classification was possible because, if p odd, these loops are centrally nilpotent. The case p = 2 was done computationally.The classification methodology that we intend to apply in this case is similar to that applied in the case p3. But in this case we have difficulties because the main loopmatching is no longer nilpotent of degree two or have more than two generators. So we have to study the A-loops commutative nilpotent of degree two with arbitrary number of generators and A-loops commutative nilpotent of degree three.

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)

SOUZA DE BARROS, DYLENE AGDA; GRISHKOV, ALEXANDER; VOJTECHOVSKY, PETR. The free commutative automorphic 2-generated loop of nilpotency class 3. COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, v. 53, n. 3, p. 16-pg., 2012-01-01. (10/16112-4)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

BARROS, Dylene Agda Souza de. Sobre a classificação dos A-loops comutativos de ordem 'p POT 3' e 'p POT 4'. 2013. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.