A well-known result of P. Hall
shows that finite solvable groups may be characterized by a permutability
requirement on Sylow subgroups. The notion of a generalized Sylow tower group
(GSTG) arises when this permutability condition on Sylow subgroups is replaced
by a suitable normalizer condition. In an earlier papar, one of the authors
showed that the nilpotent length of a GSTG cannot exceed the number of
distinct primes which divide the order of the group. The present investigation
utilizes the ‘type’ of a GSTG to obtain improved bounds for the nilpotent
length of a G,STG. It is also shown that a GSTG with nilpotent length
n possesses a Hall subgroup of nilpotent length n which is a Sylow tower
group.
