For an odd prime
, a
-
transposition group
is a group generated by a set of involutions such that the product of any two has order 2 or
. We first classify a family of
-geodesic transitive Cayley graphs
where
is a set of involutions and
. In this case,
is either an elementary
... [Show full abstract] abelian 2-group or a
-transposition group. Then under the further assumption that
acts quasiprimitively on the vertex set of
, we prove that: (1) if
is not
-arc transitive, then this quasiprimitive action is the holomorph affine type; (2) if
is a
-transposition group and
is a conjugacy class, then
and
is
-arc transitive.