Groups of Prime Power Order. Volume 1

By Yakov Berkovich

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.

• Format: Hardcover
• Language: English
• ISBN: 3110204185
• ISBN13: 9783110204186
• Release Date: November 2008
• Publisher: de Gruyter
• Length: 532 Pages
• Weight: 2.30 lbs.
• Dimensions: 1.1" x 6.7" x 9.6"
• Age Range: 22 years and up
• Grade Range: Postsecondary