Classification of minimal Frobenius hypermaps - Yuan, Kai (Ars mathematica contemporanea, 2023)
In this paper, we give a classification of orientably regular hypermaps with an automorphism group that is a minimal Frobenius group. A Frobenius group ?$G$? is called minimal if it has no nontrivial normal subgroup ?$N$? such that ?$G/N$? is a Frobenius group. An orientably regular hypermap ?$\mathcal{H}$? is called a Frobenius hypermap if ?$Aut (\mathcal{H})$? acting on the hyperfaces is a Frobenius group. A minimal Frobenius hypermap is a Frobenius hypermap whose automorphism group is a minimal Frobenius group with cyclic point stabilizers. Every Frobenius hypermap covers a minimal Frobenius hypermap. The main theorem of this paper generalizes the main result of A. B. D'Azevedo and M. E. Fernandes Eur. J. Comb. 32, No. 2, 233242 (2011).
Keywords: Frobenius group; Frobenius hypermap; Frobeniusov hiperzemljevid; Frobeniusova grupa