00325 - Theory of Groups of Finite Order [Burnside, 1st edition 1897].pdf

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THEORY OF GROUPS
OF
FINITE ORDER.
Uonbon:
C.
J.
CLAY
AND
SONS,
CAMBRIDGE UNIVERSITY PRESS WAREHOUSE,
AVE MARIA LANE.
&la!!gol:u: 263, ARGYLE STREE'l'.
1Leip}ig: F. A. BROCKHAUS.
fflel:u
~ark:
THE MACMILLAN COMPANY.
THEORY
OF
GROUPS
OF
FINITE
ORDER
BY
W. BURNSIDE, M.A., F.R.S.,
LATE FELLOW OF PEMBROKE COLLEGE, CAMBRIDGE ;
PROFESSOR OF MATHEMATICS AT THE ROYAL NAVAL COLLEGE, GREENWICH.
CAMBRIDGE:
.A.T THE UNIVERSITY PRESS.
1897
[All Rights reserved.]
Q!:ambtilJgt:
PRINTED BY
J.
AND C. F. OLAY,
AT THE UNIVERSITY PRESS.
PREFACE.
HE theory of groups of finite order may be said to date
from the time of Qauchy. To him are due the first
attempts at classification with a view to forming a theory from
a number of isolated facts. Galois introduced into the theory
the exceedingly important idea of a self-conjugate sub-group,
and the corresponding division of groups into simple and c()m-
posite. Moreover, by shewing that to every equation of finite
degree there corresponds a group of finite order on which .
all the properties of the equation depend, Galois indicated
how far reaching the applications of the theory might be, and
thereby contributed greatly, if indirectly, to its subsequent
developement.
Many additions were made, mainly by French mathe-
maticians, during the middle part of the century. The first
connected exposition of the theory was given in the third
edition of
M.
Serret's
"Cours d'Algebre Superieure,"
which was
published in 1866. This was follow·ed. in 1870 by
M.
Jordan's
"Traite des substitutions et des equations algebriques."
The
greater part of
M.
Jordan's treatise is devoted to a develope-
ment of the ideas of Galois and to their application to the
theory of equations.
No ·considerable progress in the theory, as apart from its
applications, was made till the appearance in 1872 of Herr
Sylow's memoir
"Theoremes sur les groupes de substitutions"
in the fifth volume of the
Mathematische Annalen.
Since the
date of this memoir, but more especially in recent years, the
theory has advanced continuously.
In 1882 appeared Herr Netto's ''
Hubstitutionentheorie und
T

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