This is the first of three volumes of a comprehensive and elementary treatment of finite p -group theory. Topics covered in this monograph include: (a) counting of subgroups, with almost all main counting theorems being proved, (b) regular p -groups and regularity criteria, (c) p -groups of maximal class and their numerous characterizations, (d) characters of p -groups, (e) p -groups with large Schur multiplier and commutator subgroups, (f) ( p 1)-admissible Hall chains in normal subgroups, (g) powerful p -groups, (h) automorphisms of p -groups, (i) p -groups all of whose nonnormal subgroups are cyclic, (j) Alperin's problem on abelian subgroups of small index.

The book is suitable for researchers and graduate students of mathematics with a modest background on algebra. It also contains hundreds of original exercises (with difficult exercises being solved) and a comprehensive list of about 700 open problems.

Autorentext

Yakov Berkovich , University of Haifa, Israel.