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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2016, номер 1, страницы 64–69
(Mi basm412)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Linear groups that are the multiplicative groups of neofields
Anthony B. Evans Wright State University
Аннотация:
A neofield $N$ is a set with two binary operations, addition and multiplication, for which $N$ is a loop under addition with identity $0$, the nonzero elements of $N$ form a group under multiplication, and both left and right distributive laws hold. Which finite groups can be the multiplicative groups of neofields? It is known that any finite abelian group can be the multiplicative group of a neofield, but few classes of finite nonabelian groups have been shown to be multiplicative groups of neofields. We will show that each of the groups $GL(n, q)$, $PGL(n, q)$, $SL(n, q)$, and $PSL(n, q)$, $q$ even, $q\ne2$, can be the multiplicative group of a neofield.
Ключевые слова и фразы:
neofield, linear group, orthomorphism, near orthomorphism.
Поступила в редакцию: 23.11.2015
Образец цитирования:
Anthony B. Evans, “Linear groups that are the multiplicative groups of neofields”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2016, no. 1, 64–69
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/basm412 https://www.mathnet.ru/rus/basm/y2016/i1/p64
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