Characterising locally finite groups satisfying the strong Sylow Theorem for the prime p

This publication presents the most essential portions of the author's German Diplomarbeit of 1984 and a "sprinkling" of new considerations and results as well which earnestly try to propose coming directions for (timeless and eternal) Sylow theory in (locally) finite groups. The 2nd edition provides quite a number of clarifications and corrections and adds the Chapter "Endnotes" which describes new proofs of historic relevance for the theorems of Lagrange and Cauchy on finite groups.