TY - JOUR
T1 - Vertex stabilizers of locally s-arc transitive graphs of pushing up type
AU - Parker, Chris
AU - van Bon, John
N1 - Not yet published as of 22/04/2024.
PY - 2024/4/4
Y1 - 2024/4/4
N2 - Suppose that Δ a thick, locally finite and locally s-arc transitive G-graph with s≥4. For a vertex z in Δ, let Gz be the stabilizer of z and G[1]z be the kernel of the action of Gz on the neighbours of z. We say Δ is of pushing up type provided there exists a prime p and a 1-arc (x,y) such that CGz(Op(G[1]z))≤Op(G[1]z) for z∈{x,y} and Op(G[1]x)≤Op(G[1]y). We show that if Δ is of pushing up type, then Op(G[1]x) is elementary abelian and Gx/G[1]x≅X with PSL2(pa)≤X≤PΓL2(pa).
AB - Suppose that Δ a thick, locally finite and locally s-arc transitive G-graph with s≥4. For a vertex z in Δ, let Gz be the stabilizer of z and G[1]z be the kernel of the action of Gz on the neighbours of z. We say Δ is of pushing up type provided there exists a prime p and a 1-arc (x,y) such that CGz(Op(G[1]z))≤Op(G[1]z) for z∈{x,y} and Op(G[1]x)≤Op(G[1]y). We show that if Δ is of pushing up type, then Op(G[1]x) is elementary abelian and Gx/G[1]x≅X with PSL2(pa)≤X≤PΓL2(pa).
UR - https://link.springer.com/journal/10801
U2 - 10.48550/arXiv.2312.02627
DO - 10.48550/arXiv.2312.02627
M3 - Article
SN - 0925-9899
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
ER -