Moufang loops and related groups

• Grant number: 14/08964-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2014
• End date: September 30, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Alexandre Grichkov
• Grantee: Ilia Gorshkov
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The research project is for the post-Doc program in group theory and loop the-ory. Spectra of finite semi simple groups will be investigated. Information about spectra isuseful in applications for finite simple groups and in further studies of finite and locally finitegroups. Tompson's conjecture on conjugacy classes and S 3 conjecture will be considered.Group G is called triality group if G admits the S 3 as a group of automorphisms with someadditional conditions on the action. Glauberman and Doro discovered a connection betweengroups with triality and Moufang loops. Using this connection we will investigate Cheinconjecture for Moufang loops, a conjecture on Frattini subloop, and some other conjecturesand open problems related to Bol and Moufang loops. The results of the project can beused in other studies of group theory and its applications.

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)

GORSHKOV, I. B.; GRISHKOV, A. N.. ON RECOGNITION BY SPECTRUM OF SYMMETRIC GROUPS. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, v. 13, p. 111-121, 2016. (14/08964-1)

GORSHKOV, I. B.; GRISHKOV, A. N.; ZAVARNITSINE, A. V.. On Two Problems Related to Associators of Moufang Loops. MATHEMATICAL NOTES, v. 101, n. 1-2, p. 230-233, JAN 2017. (14/08964-1)

GORSHKOV, I. B.; MASLOVA, V, N.. FINITE ALMOST SIMPLE GROUPS WHOSE GRUENBERG-KEGEL GRAPHS COINCIDE WITH GRUENBERG-KEGEL GRAPHS OF SOLVABLE GROUPS. Algebra and Logic, v. 57, n. 2, p. 115-129, JUN 2018. (14/08964-1)