J. Aust. Math. Soc.
80 (2006), 4563

Seminormal and subnormal subgroup lattices for transitive permutation groups

Cheryl E. Praeger
School of Mathematics and Statistics
The University of Western Australia
35 Stirling Highway
Crawley WA 6009
Australia
praeger@maths.uwa.edu.au



Abstract

Various lattices of subgroups of a finite
transitive permutation group G
can be used to define a set of `basic'
permutation groups associated with
G
that are analogues of composition factors for
abstract finite groups. In particular,
G
can be embedded in an iterated wreath product of
a chain of its associated basic permutation
groups. The basic permutation groups
corresponding to the lattice
of all subgroups of G
containing a given point stabiliser are a set of
primitive permutation groups. We introduce two
new subgroup lattices contained in
, called the seminormal subgroup lattice and the
subnormal subgroup lattice. For these lattices
the basic permutation groups are quasiprimitive
and innately transitive groups, respectively.

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