Finite geometries, its automorphisms and related algebraic systems.
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Finite geometries and related loops and quasigroups
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| Author(s): |
Diana Rasskazova
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2018-09-12 |
| Examining board members: |
Ivan Chestakov;
Henrique Guzzo Junior;
Plamen Emilov Kochloukov;
Alexandr Kornev;
Dmitry Logachev
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| Advisor: | Ivan Chestakov; Alexandre Grichkov |
| Abstract | |
This work is about finite geometries with 3 or 4 points on every line and related loops and quasigroups. In the case of 3 points on any line we describe the structure of free loops in the variety of corresponding Steiner loops and we calculate the group of automorphisms of free Steiner loop with three generators. We describe the structure of nilpotent class two Steiner loops and classifiy all such loops with three generators. In the case of 4 points on a line we constructe new series of such geometries as central extension of corresponding non-commutative Steiner quasigroups. We conjecture that those geometries are universal in some sense. (AU) | |
| FAPESP's process: | 15/17611-8 - Finite geometries, its automorphisms and related algebraic systems. |
| Grantee: | Diana Rasskazova |
| Support Opportunities: | Scholarships in Brazil - Doctorate |