Тип публикации: статья из журнала
Год издания: 2019
Идентификатор DOI: 10.26516/1997-7670.2019.29.107
Ключевые слова: finite Dixon near-field, quasifield, semi field, Moufang loop, Moufang quasifield, Semifield
Аннотация: The structure of finite quasi-fields with associative degrees is investigated. These are, above all, associative quasi fields, called near-fields. These also include the Moufang quasi fields which have loops of nonzero elements are, by definition, loops i The structure of finite quasi-fields with associative degrees is investigatedПоказать полностью. These are, above all, associative quasifields, called near-fields. These also include the Moufang quasifields which have loops of nonzero elements are, by definition, loops introduced by Ruth Moufang in 1935. The paper presents the main definitions associated with quasifields. It is shown that identity element of any finite (right) quasifield Q generates a simple subfield P, and Q is always a one-sided module over P, and a two-way — is not always. As a result, found new proof of a well-known statement: a simple subfield of a finite semifield always lies in the center. At the same time, the finite near-fields with a simple subfield that does not lie in the center. Famous the question of maximal subfields of finite quasifields is completely solved for a class of finite near-fields of order pr with prime numbers p and r. In solving the questions about maximal subfields and spectra of group orders of nonzero elements of finite Moufang quasifields, it is proposed to use the well-known analogues of the group-theoretic theorems of Lagrange and Sylow. All possible two-digit orders of the proper Moufang quasifields are listed. © 2019 CONICET - Emiliano Aldegani. All rights reserved.
Журнал: BULLETIN OF IRKUTSK STATE UNIVERSITY-SERIES MATHEMATICS
Выпуск журнала: Vol. 29
Номера страниц: 107-119
ISSN журнала: 19977670
Место издания: IRKUTSK
Издатель: IRKUTSK STATE UNIV