Geodesic
Automorphism groups of cyclotomic schemes over finite near-fields
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1271-1282.

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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. 
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D. V. Churikov; A. V. Vasil'ev. Automorphism groups of cyclotomic schemes over finite near-fields. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1271-1282. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a37/

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