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17):~t? L It CIFDr- ! wei! unsre Weisheit Einfalt ist, From
"Lohengrin", Richard Wagner At the time of the appearance of the
first volume of this work in 1967, the tempestuous development of
finite group theory had already made it virtually impossible to
give a complete presentation of the subject in one treatise. The
present volume and its successor have therefore the more modest aim
of giving descriptions of the recent development of certain
important parts of the subject, and even in these parts no attempt
at completeness has been made. Chapter VII deals with the
representation theory of finite groups in arbitrary fields with
particular attention to those of non-zero charac teristic. That
part of modular representation theory which is essentially the
block theory of complex characters has not been included, as there
are already monographs on this subject and others will shortly
appear. Instead, we have restricted ourselves to such results as
can be obtained by purely module-theoretical means.
Und dann erst kommt der "Ab -ge - sa. ng\' da. /3 der nidlt kurz
und nicht zu la. ng, From "Die Meistersinger von Nurnberg," Richard
Wagner This final volume is concerned with some of the developments
of the subject in the 1960's. In attempting to determine the simple
groups, the first step was to settle the conjecture of Burnside
that groups of odd order are soluble. The proof that this
conjecture was correct is much too long and complicated for
presentation in this text, but a number of ideas in the early
stages of it led to a local theory of finite groups, so me aspects
of which are discussed in Chapter X. Much of this discussion is a
con tinuation of the theory of the transfer (see Chapter IV), but
we also introduce the generalized Fitting subgroup, which played a
basic role in characterization theorems, that is, in descriptions
of specific groups in terms of group-theoretical properties alone.
One of the earliest and most important such characterizations was
given for Zassenhaus groups; this is presented in Chapter XI.
Characterizations in terms of the centralizer of an involution are
of particular importance in view of the theorem of Brauer and
Fowler. In Chapter XII, one such theorem is given, in which the
Mathieu group 9J'l1l and PSL(3, 3) are characterized."
University Of Chicago Department Of Mathematics.
University Of Chicago Department Of Mathematics.
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