On Abelian subgroups of p-groups

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