This book is a somewhat expanded version of a graduate course in finite
group theory that I often teach at the University of Wisconsin. I offer this
course in order to share what I consider to be a beautiful subject with as
many people as possible, and also to provide the solid background in pure
group theory that my doctoral students need to carry out their thesis work
in representation theory.
The focus of group theory research has changed profoundly in recent
decades. Starting near the beginning of the 20th century with the work of
W. Burnside, the major problem was to find and classify the finite simple
groups, and indeed, many of the most significant results in pure group theory
and in representation theory were directly, or at least peripherally, related to
this goal. The simple-group classification now appears to be complete, and
current research has shifted to other aspects of finite group theory including
permutation groups, p-groups and especially, representation theory.
It is certainly no less essential in this post-classification period that
group-theory researchers, whatever their subspecialty, should have a mas-
tery of the classical techniques and results, and so without attempting to
be encyclopedic, I have included much of that material here. But my choice
of topics was largely determined by my primary goal in writing this book,
which was to convey to readers my feeling for the beauty and elegance of
finite group theory.
Given its origin, this book should certainly be suitable as a text for a
graduate course like mine. But I have tried to write it so that readers would
also be comfortable using it for independent study, and for that reason, I
have tried to preserve some of the informal flavor of my classroom. I have
tried to keep the proofs as short and clean as possible, but without omitting
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