Suppose that Delta is a thick, locally finite and locally s-arc transitive G-graph with s &gt;= 4. For a vertex z in Delta, let G(z) be the stabilizer of z and G(z)([1]) be the kernel of the action of G(z) on the neighbours of z. We say Delta is of pushing up type provided there exists a prime p and a 1-arc (x,y) such that C-Gz(O-p(G(z)([1])))&lt;= O-p(G(z)([1])) for z is an element of{x,y} and Op(G(x)([1]))&lt;= O-p(G(y)([1])). We show that if Delta is of pushing up type, then O-p(G(x)([1])) is elementary abelian and G(x)/G(x)([1])congruent to X with PSL2(p(a))&lt;= X &lt;= P Gamma L-2(p(a)).

### Vertex stabilizers of locally s-arc transitive graphs of pushing up type

#### Abstract

Suppose that Delta is a thick, locally finite and locally s-arc transitive G-graph with s >= 4. For a vertex z in Delta, let G(z) be the stabilizer of z and G(z)([1]) be the kernel of the action of G(z) on the neighbours of z. We say Delta is of pushing up type provided there exists a prime p and a 1-arc (x,y) such that C-Gz(O-p(G(z)([1])))<= O-p(G(z)([1])) for z is an element of{x,y} and Op(G(x)([1]))<= O-p(G(y)([1])). We show that if Delta is of pushing up type, then O-p(G(x)([1])) is elementary abelian and G(x)/G(x)([1])congruent to X with PSL2(p(a))<= X <= P Gamma L-2(p(a)).
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2024
Locally s-arc transitive graphs
Group amalgams
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/20.500.11770/370957`
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