In this paper two different
generalizations of Sylow tower groups are studied. In Chapter I the notion of a
k-tower group is introduced and a bound on the nilpotence length (Fitting height) of
an arbitrary finite solvable group is found. In the same chapter a different proof to a
theorem of Baer is given; and the list of all minimal-not-Sylow tower groups is
obtained.
Further results are obtained on a different generalization of Sylow tower groups,
called Generalized Sylow Tower Groups (GSTG) by J. Derr. It is shown that the
class of all GSTG’s of a fixed complexion form a saturated formation, and a structure
theorem for all such groups is given.
