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This article is cited in 3 scientific papers (total in 4 papers)
Mathematical logic, algebra and number theory
Automorphism groups of cyclotomic schemes over finite near-fields
D. V. Churikova, A. V. Vasil'evba a Novosibirsk State University, ul. Pirogova, 2, 630090, Novosibirsk, Russia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
Abstract:
We prove that apart from a finite number of known exceptions the automorphism group of a nontrivial cyclotomic scheme over a finite near-field $\mathbb{K}$ is isomorphic to a subgroup of the group ${\operatorname{A\Gamma L}}(1,\mathbb{F})$, where $\mathbb{F}$ is a field with $|\mathbb{F}|=|\mathbb{K}|$. Moreover, we obtain that the automorphism group of such a scheme is solvable if the base group of the scheme is
solvable.
Keywords:
near-field, cyclotomic scheme, automorphism group of a scheme, $2$-closure of a permutation group, $\frac{3}{2}$-transitive permutation groups.
Received October 7, 2016, published December 23, 2016
Citation:
D. V. Churikov, A. V. Vasil'ev, “Automorphism groups of cyclotomic schemes over finite near-fields”, Sib. Èlektron. Mat. Izv., 13 (2016), 1271–1282
Linking options:
https://www.mathnet.ru/eng/semr749 https://www.mathnet.ru/eng/semr/v13/p1271
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