Theory and applications of finite groups, by G.A. Miller, H. F. Blichfeldt [and] L. E. Dickson.

PREFACE

THE aim of this book is to present in a unified manner the
more fundamental aspects of finite groups and their applications,
and at the same time to preserve the advantage which arises
when each branch of an extensive subject is written by one who
has long specialized in that branch.
To secure unification, the three authors planned the book
after various conferences and extensive correspondence, while
each read and commented upon both the MS. and proof-sheets
of the parts by the remaining authors. However, the influence
of each author upon the other two has been mainly of editorial
character, so that the individuality of the authorship of each
part remains intact.
Part I, written by G. A. Miller, gives in the first two chapters
various concrete examples of groups and an elementary presentation of the most fundamental theorems on groups of substitutions. These two chapters prepare the way, by easy stages,
for the formal developments in the theory of abstract groups,
to which the remaining six chapters of Part I are devotedo
A reader who wishes to proceed as early as possible to the
phases of group theory presented in Part II or Part III will
find that the prerequisites for either of the latter parts are met
by these first two chapters of Part I, with the exception that
also ~ 22, ~ 27, ~ 48 are needed for the last half of Part II, while
~ 68 is needed for Part III.
Chapter III is devoted to a development of fundamental
theorems of abstract group theory and to the establishment of
a logical connection between this theory and the theory of substitution groups. A (1,1) correspondence between the abstract
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