Graphical Frobenius representations of non-abelian groups

Gábor Korchmáros, Gábor Péter Nagy

Abstract


A group G has a Frobenius graphical representation (GFR) if there is a simple graph Γ whose full automorphism group is isomorphic to G acting on the vertices as a Frobenius group. In particular, any group G with a GFR is a Frobenius group and Γ is a Cayley graph. By very recent results of Spiga, there exists a function f such that if G is a finite Frobenius group with complement H and |G| > f(|H|) then G admits a GFR. This paper provides an infinite family of graphs that admit GFRs despite not meeting Spiga’s bound. In our construction, the group G is the Higman group A(f, q0) for an infinite sequence of f and q0, having a nonabelian kernel and a complement of odd order.


Keywords


Cayley graph, Frobenius group, Suzuki 2-group, Frobenius graphical representation

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DOI: https://doi.org/10.26493/1855-3974.2154.cda

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications