The 2-length of a finite solvable group

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In this paper the relationship between the 2-length [...] and the 2-exponent [...] of a finite solvable group G is studied. It is shown that [...] - 1 provided that [...]. The special case of groups satisfying [...] = 2, i.e., groups whose Sylow 2-groups are of exponent 4, is investigated to determine whether [...] in this case. This question is not answered but it is shown that a certain normal subgroup (which may be the whole group) satisfies [...]. In addition if all the elements of order 4 are contained in this subgroup, then [...] for the whole group as well. As an application of this last result, it is proved that [...] in a group of exponent 12