The aim of this book is to serve both as an introduction to
profinite groups and as a reference for specialists in some areas
of the theory. The book is reasonably self-contained. Profinite
groups are Galois groups. As such they are of interest in algebraic
number theory. Much of recent research on abstract infinite groups
is related to profinite groups because residually finite groups are
naturally embedded in a profinite group. In addition to basic facts
about general profinite groups, the book emphasizes free
constructions (particularly free profinite groups and the structure
of their subgroups). Homology and cohomology is described with a
minimum of prerequisites.
This second edition contains three new appendices dealing with a
new characterization of free profinite groups, presentations of
pro-p groups and a new conceptually simpler approach to the proof
of some classical subgroup theorems. Throughout the text there are
additions in the form of new results, improved proofs,
typographical corrections, and an enlarged bibliography. The list
of open questions has been updated; comments and references have
been added about those previously open problems that have been
solved after the first edition appeared.
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