Abstract.
Let G be a transitive permutation group acting on a finite set
and let P be the stabilizer in G of a point in . We say
that G is primitive rank 3 on if P is maximal in G and
P has exactly three orbits on . For any subgroup H of G,
we denote by 
the permutation character (or permutation
module) over 
of G on the cosets 
. Let H and K
be subgroups of G. We say 
if 
is a
character of G. Also a finite group G is called nearly simple
primitive rank 3 on if there exists a quasi-simple group L
such that 
and G acts as a
primitive rank 3 permutation group on the cosets of some subgroup
of L. In this paper we classify all maximal subgroups M of a
nearly simple primitive rank 3 group G of type
, 
, acting on an L-orbit of
non-singular points of the natural module for L such that
, where P is the stabilizer of a non-singular
point in . This result has an application to the study of
minimal genera of algebraic curves which admit group actions.
© 2013 by Walter de Gruyter Berlin Boston
