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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, номер 1, страницы 122–128
(Mi basm527)
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Research articles
Loops with invariant flexibility under the isostrophy
Parascovia Syrbua, Ion Grecub a Moldova State University, 60 Mateevici str., Chisinau, MD-2009, Rep. of Moldova
b Moldovan-Finnish High School, 59 Calea Iesilor str., Chisinau, MD-2069, Rep. of Moldova
Аннотация:
The question "Are the loops with universal (i.e. invariant under the isotopy of loops) flexibility law $xy\cdot x = x\cdot yx$, middle Bol loops?" is open in the theory of loops. If this conjecture is true then the loops for which all isostrophic loops are flexible are Moufang loops. In the present paper we prove that commutative loops with invariant flexibility under the isostrophy of loops are Moufang loops. In particular, we obtain that commutative $IP$-loops with universal flexibility are Moufang loops.
Ключевые слова и фразы:
loop with universal flexibility, middle Bol loop, Moufang loop, isostrophy.
Поступила в редакцию: 02.05.2020
Образец цитирования:
Parascovia Syrbu, Ion Grecu, “Loops with invariant flexibility under the isostrophy”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 1, 122–128
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/basm527 https://www.mathnet.ru/rus/basm/y2020/i1/p122
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Страница аннотации: | 98 | PDF полного текста: | 31 | Список литературы: | 12 |
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