Groups of Prime Power Order. Volume 1

von Yakov Berkovich

512 Seiten, Hardcover

Kurzbeschreibung des Verlags

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.

• Reihe: De Gruyter Expositions in Mathematics
• ISBN: 9783110204186
• Sprache: Englisch
• Erscheinungsdatum: 17.11.2008
• Genre: Mathematik/Allgemeines, Lexika
• Verlag: De Gruyter