De Gruyter Expositions in Mathematics 56

Abstract

This is the third volume of a comprehensive and elementary treatment of finite p -group theory. Topics covered in this volume: impact of minimal nonabelian subgroups on the structure of p -groups, classification of groups all of whose nonnormal subgroups have the same order, degrees of irreducible characters of p -groups associated with finite algebras, groups covered by few proper subgroups, p -groups of element breadth 2 and subgroup breadth 1, exact number of subgroups of given order in a metacyclic p -group, soft subgroups, p -groups with a maximal elementary abelian subgroup of order p 2 , p -groups generated by certain minimal nonabelian subgroups, p -groups in which certain nonabelian subgroups are 2-generator. The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes.