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Published by the School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, U.K.
Founding editor: K. W. Gruenberg
Current editor: P. J. Cameron
Susan McKay, Finite p-groups
ix + 102 pp., £7
P&P £1 (in U.K.), £2 (other countries)
ISBN 0 902480 17 0
The theory of finite p-groups has changed direction and advanced considerably over the past twenty years. These lecture notes cover the material in an M.Sc. course given in Queen Mary, University of London. Their aim is to collect together the classical theory and some more recent ideas in one coherent account. They will enable a beginning research student to have the background knowledge needed to embark on research this area.
After introductory chapters on finite groups, on p-groups, and on commutator collection, there are chapters on three major topics in the theory: regular p-groups, powerful p-groups, and p-groups of maximal class.
As well as providing suitable material for a course on p-groups, the notes are essential preliminary reading for the forthcoming book by the author and Charles Leedham-Green on p-groups of bounded coclass.
Exercises are included in the text at regular intervals, and a list of notation is included as well as an index.
From the review by A. Caranti in Zentralblatt für Mathematik:
These notes, written by a leading expert in the field, live up to their promises, and represent a solid revisitation of the classical theory, and an excellent introduction to current research in the field.
The table of contents and a list of corrections are available in PDF format.
Peter J. Cameron
21 February 2002.