This is a continuation of our note (J. Algebra 186 (1996), 120-131). W
e generalize and present simplified proofs almost all elementary lemma
s from Section 8 of the Odd Order Paper. In many places we use Hall's
enumeration principle and other simple combinatorial arguments. A numb
er of related results are proved as well. Some open questions are pose
d. (C) 1998 Academic Press.