Graphical Frobenius representations of non-abelian groups

Gábor Korchmáros, Gábor Péter Nagy
2020 Ars Mathematica Contemporanea  
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
more » ... meeting Spiga's bound. In our construction, the group G is the Higman group A(f, q 0 ) for an infinite sequence of f and q 0 , having a nonabelian kernel and a complement of odd order.
doi:10.26493/1855-3974.2154.cda fatcat:xie5pit7e5gb5gdufc2yswuwvq