Frobenius group is a transitive permutation group that is not regular and such that only the identity fixes more than one point. A digraphical, respectively graphical, Frobenius representation, DFR and GFR for short, of a Frobenius group F is a digraph, respectively graph, whose automorphism group as a group of per- mutations of the vertex set is F. The problem of classifying which Frobenius groups admit a DFR and GFR has been proposed by Mark Watkins and Thomas Tucker and is a natural extension of the problem of classifying which groups that have a digraphical, respectively graphical, regular representation. In this paper, we give a partial answer to a question of Mark Watkins and Thomas Tucker concerning Frobenius representations: “All but finitely many Frobenius groups with a given Frobenius complement have a DFR”.
Spiga, P. (2018). On the existence of frobenius digraphical representations. ELECTRONIC JOURNAL OF COMBINATORICS, 25(2) [10.37236/7097].
On the existence of frobenius digraphical representations
Spiga P.
2018
Abstract
Frobenius group is a transitive permutation group that is not regular and such that only the identity fixes more than one point. A digraphical, respectively graphical, Frobenius representation, DFR and GFR for short, of a Frobenius group F is a digraph, respectively graph, whose automorphism group as a group of per- mutations of the vertex set is F. The problem of classifying which Frobenius groups admit a DFR and GFR has been proposed by Mark Watkins and Thomas Tucker and is a natural extension of the problem of classifying which groups that have a digraphical, respectively graphical, regular representation. In this paper, we give a partial answer to a question of Mark Watkins and Thomas Tucker concerning Frobenius representations: “All but finitely many Frobenius groups with a given Frobenius complement have a DFR”.File | Dimensione | Formato | |
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