Graphical Frobenius representations of non-abelian groups

Gábor Korchmáros; Gábor P. Nagy

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arXiv · 1909.03690

Graphical Frobenius representations of non-abelian groups

Gábor Korchmáros·Gábor P. Nagy

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Abstract

A group $G$ has a Frobenius graphical representation (GFR) if there is a simple graph $\varGamma$ whose full automorphism group is isomorphic to $G$ and it acts on vertices as a Frobenius group. In particular, any group $G$ with GFR is a Frobenius group and $\varGamma$ is a Cayley graph. The existence of an infinite family of groups with GFR whose Frobenius kernel is a non-abelian $2$-group has been an open question. In this paper, we give a positive answer by showing that the Higman group $A(f,q_0)$ has a GFR for an infinite sequence of $f$ and $q_0$.

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BibTeX RIS

Gábor Korchmáros, Gábor P. Nagy. 2019-09-09. Graphical Frobenius representations of non-abelian groups. https://arxiv.org/abs/1909.03690

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