Automorphism groups of cyclotomic schemes over finite near-fields

D. V. Churikov ; A. V. Vasil'ev

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1271-1282

Résumé

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.

Détail

Keywords: near-field, cyclotomic scheme, automorphism group of a scheme, $2$-closure of a permutation group, $\frac{3}{2}$-transitive permutation groups.