دانلود کتاب Fundamentals of the Theory of Groups

This book consists of notes from lectures given by the authors at
Novosibirsk University from 1968 to 1970. Their intention was to set forth just the
fundamentals of group theory, avoiding excessive detail and skirting the
quagmire of generalizations (however a few generalizations are nonetheless
considered—see the last sections of Chapters 6 and 7). We hope that the
student desiring to work in the theory of groups, having become acquainted
with its fundamentals from these notes, will quickly be able to proceed to the
specialist literature on his chosen topic.
The authors striven not to cross the boundary between abstract and scholastic
group theory, elucidating difficult concepts by means of simple examples
wherever possible. Four types of examples accompany the theory: numbers
under addition, numbers under multiplication, permutations, and matrices.
For understanding the basic text, knowledge gained from a general course in
algebra will suffice; more special facts are used at times in the examples. The
examples and exercises are in part used in the basic text, so that a reading of
their statements should not be omitted, nor their solution postponed for too
long. Solutions are included with some of these exercises. We were guided in
our nomenclature by the principle of a reasonable minimum of basic terms,
which required small departures from the prevailing terminology—these are
noted at the appropriate places in the text.