Theory of Groups of Finite Order

An unabridged republication of the classic 1911 edition, this volume constitutes both a great historical contribution to mathematical literature and a basic reference book in its field. Suitable for advanced undergraduates and graduate students in mathematics as well as historians of mathematics, the introductory treatment was hailed by International Mathematical News as "more easily comprehensible than most other books on the subject," and as "a classic work, extraordinarily rich," by Elemente der Mathematik.
After introducing permutation notation and presenting the definition of a group, author William Burnside discusses the simpler properties of groups that are independent of their modes of representation; composition-series of groups; isomorphism of a group with itself; Abelian groups; groups whose orders are the powers of primes; and Sylow's theorem. Permutation groups and groups of linear substitutions receive an extensive treatment; two chapters are devoted to the graphic representation of groups, and the closing chapter examines congruence groups. Forty-five pages of notes at the back of the book offer ample treatment of special topics.

British mathematician William Burnside (1852–1927) studied at Cambridge University and was later appointed Professor of Mathematics at the Royal Naval College in Greenwich, UK, where he spent his career. Burnside published more than 150 papers on mathematical topics. Cambridge University Press published the first edition of his classic book, Theory of Groups of Finite Order, in 1897 and in an expanded second edition in 1911. For the next 40-plus years, this book was the classic introduction to group theory, a worthy ancestor of Marshall Hall's The Theory of Groups, first published in 1959 and also now reprinted by Dover.

I. On PermutationsII. The Definition of a GroupIII. On the Simpler Properties of a Group which are Independent of its Mode of RepresentationIV. Further Properties of a Group Which Are Independent of its Mode of RepresentationV. On the Composition-Series of a GroupVI. On the Isomorphism of a Group with ItselfVII.On Abelian GroupsVIII. On Groups Whose Orders are the Powers of PrimesIX. On Sylow's TheoremX. On Permutation-Groups: Transitive and Intransitive Groups: Primitive and Imprimitive GroupsXI. On Permutation-Groups: Transitivity and Primitivity: (Concluding Properties)XII. On the Representation of a Group of Finite Order as a Permutation-GroupXIII. On Groups of Linear Substitutions; Reducible and Irreducible GroupsXIV. On the Representation of a Group of Finite Order as a Group of Linear SubstitutionsXV. On Group-CharacteristicsXVI. Some Applications of the Theory of Groups of Linear Substitutions and of Group-CharacteristicsXVII. On the Invariants of Groups of Linear SubstitutionsXVIII. On the Graphical Representation of a GroupXIX. On the Graphical Representation of Groups: Groups of Genus Zero and Unity: Cayley's Colour-GroupsXX. On Congruence GroupsNotes (A through O)Index of Technical TermsIndex of Authors QuotedGeneral Index