One measure of the
structure of a finite solvable group G is its p-length lp(G). A problem connected with
this measure is to obtain an upper bound for lp(G) in terms of ep(G), which
is a numerical invariant of the Sylow p-subgroups of G. This problem has
been solved but the best-possible result is not known for p = 2. The main
result of this paper is that l2(G) ≦ 2e2(G) − 1, which is an improvement on
earlier results. A secondary objective of this paper is to investigate finite
solvable groups in which the Sylow 2-group is of exponent 4. In particular it is
proved that if G is a finite group of exponent 12, then the 2-length is at most
2.
