ON GROUPS OF ODD ORDER AND RANK $\[ \le 2\]$

The least commonmultiple of dimensions of chief factors of a finite solvable group is called the rank of the group. The groups of odd order with trivial Fratttini subgroups all of whose subgroups but itself have ranks are completely determined (Theorem A). For an odd number a necessary and sufficient condition for the groups of order n all to be of rank $\ \le 2\]$ is obtained (Theorem B).