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- W4289754157 abstract "It is known that there are precisely three transitive permutation groups of degree $6$ that admit an invariant partition with three parts of size $2$ such that the kernel of the action on the parts has order $4$; these groups are called $A_4(6)$, $S_4(6d)$ and $S_4(6c)$. For each $Lin {A_4(6), S_4(6d), S_4(6c)}$, we construct an infinite family of finite connected $6$-valent graphs ${Gamma_n}_{nin mathbb{N}}$ and arc-transitive groups $G_n le rm{Aut}(Gamma_n)$ such that the permutation group induced by the action of the vertex-stabiliser $(G_n)_v$ on the neighbourhood of a vertex $v$ is permutation isomorphic to $L$, and such that $|(G_n)_v|$ is exponential in $|rm{V}(Gamma_n)|$. These three groups were the only transitive permutation groups of degree at most $7$ for which the existence of such a family was undecided. In the process, we construct an infinite family of cubic $2$-arc-transitive graphs such that the dimension of the $1$-eigenspace over the field of order $2$ of the adjacency matrix of the graph grows linearly with the order of the graph." @default.
- W4289754157 created "2022-08-04" @default.
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- W4289754157 date "2018-07-12" @default.
- W4289754157 modified "2023-10-17" @default.
- W4289754157 title "Three local actions in $6$-valent arc-transitive graphs" @default.
- W4289754157 doi "https://doi.org/10.48550/arxiv.1807.04810" @default.
- W4289754157 hasPublicationYear "2018" @default.
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