Abstract
AbstractLet $$\Delta $$
Δ
be a connected arc-transitive G-graph which is locally finite and locally quasiprimitive. Let $$\{x,y\}$$
{
x
,
y
}
be an edge of $$\Delta $$
Δ
. A relation between $$G_x^{[1]}/O_p(G_x^{[1]})$$
G
x
[
1
]
/
O
p
(
G
x
[
1
]
)
and the existence of certain normal subgroups of $$G_x^{\Delta (x)}$$
G
x
Δ
(
x
)
and $$G_{x,y}^{\Delta (x)}$$
G
x
,
y
Δ
(
x
)
is established. This is then used to determine the vertex stabilizers of a class of 2-arc-transitive graphs with trivial edge kernel.
Funder
Università della Calabria
Publisher
Springer Science and Business Media LLC
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