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K. K. Shchukin

On primitive subgroups of full affine groups of finite semi-fields

In this paper, we continue and complete the study of finite primitive groups whose stabiliser of a point contains an Abelian normal subgroup acting irreducibly (by conjugations) on an Abelian normal subgroup of the whole group. Each such group H is isomorphic to the subgroup of the full affine group of the field , where the symbol of the semi-direct product λ unites the ν-power of the cyclic group Z_p, the metacyclic group Θ, and some group of automorphisms ψ of the field . Using the Zassenhaus classification of finite semi-fields, we enumerate primitive subgroups of the full affine groups of finite semi-fields.

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 13, 12/2003
Pages: 613 - 618

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