Groups of Prime Power Order

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 p²,
• 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.