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Doctoral Thesis
DOI
Document
Author
Full name
Diana Rasskazova
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Chestakov, Ivan (President)
Guzzo Junior, Henrique
Kochloukov, Plamen Emilov
Kornev, Alexandr
Logachev, Dmitry
Title in Portuguese
Geometrias finitas, loops e quasigrupos relacionados
Keywords in Portuguese
Expanção central
Loopos de Steiner
Loopos nilpotentes
Quasigrupo de Steiner
Sitemas de Steiner
Abstract in Portuguese
Este trabalho é sobre as geométrias finitas com 3 ou 4 pontos na cada reta e os loops e qiasigrupos relacionados. Em caso de 3 pontos na cada reta descrevemos o loop de Steiner correspondente livre e calculamos o grupo de automorfismos em caso de 3 geradores livres. Além disso descrevemos os loopos de Steiner nilpotentes de clase dois e classificamos estes loopos com 3 geradores. Em caso de 4 pontos na cada reta construimos as geometrias novas atraves de expanção central de um análogo não comutativo do quasigrupo de Steiner. Temos fortes indícios que esta construção é universal em algum sentido.
Title in English
Finite geometries and related loops and quasigroups
Keywords in English
Central extension
Nilpotent loops
Steiner loops
Steiner quasigroups
Steiner systems
Abstract in English
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.
 
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Publishing Date
2019-09-25
 
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