Structure of Finite p-groups with Given Subgroups

The following main results are proved: 1) Classification of p-groups all of whose subgroups of index p (square power)are abelian. 2) Classification of p-groups with 7 involutions. 3) New proofs of some Blackburn's results (classification of minimal nonmetacyclic p-groups, classification of p-groups of odd order without normal elementary abelian subgroup of order p (power 3)). 4) Proofs of some basic counting theorems based on the new enumeration principle. 5) New proof of Ward's theorem on quaternion-free 2-groups. 6) Corrected proof of Iwasawa's theorem on the structure of modular p-groups. Our proofs are completely elementary.