On the existence of Frobenius digraphical representations
type: Item
instance of: scholarly article
title: On the existence of Frobenius digraphical representations
zbMATH Open document ID: 1390.05095
author: Pablo Spiga
published in: The Electronic Journal of Combinatorics
publication date: 2018-05-25T00:00:00Z
full work available at URL: v25i2p6
review text: Summary: A 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 permutations 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 [\textit{J. K. Doyle} et al., ``Graphical Frobenius representations'', J. Algebr. Comb. (to appear; \url{doi:10.1007/s10801-018-0814-6})]: ``All but finitely many Frobenius groups with a given Frobenius complement have a DFR''.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 6873175
zbMATH Keywords: regular representation
zbMATH Keywords: Frobenius representation
zbMATH Keywords: Cayley digraph
zbMATH Keywords: automorphism group
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6873175