Theory of Groups of Finite Order

The British mathematician William Burnside (1852-1927) and Ferdinand Georg Frobenius (1849-1917), Professor at Zurich and Berlin universities, are considered to be the founders of the modern theory of finite groups. Not only did Burnside prove many important theorems, but he also laid down lines of research for the next hundred years: two Fields Medals have been awarded for work on problems suggested by him. The Theory of Groups of Finite Order, originally published in 1897, was the first major textbook on the subject. The 1911 second edition (reissued here) contains an account of Frobenius's character theory, and remained the standard reference for many years.

Preface to the second edition
Preface to the first edition
On permutations
The definition of a group
On the simpler properties of a group which are independent of its mode of representation
Further properties of a group which are independent of its mode of representation
On the composition-series of a group
On the isomorphism of a group within itself
On Abelian groups
On groups whose orders are the powers of primes
On Sylow's theorem
On permutation-groups: transitive and intransitive groups
On permutation-groups: transitivity and primitivity
On the representation of a group of finite order as a permutation-group
On groups of linear substitutions
On the representation of a group of finite order as a group of linear substitutions
On group-characteristics
Some applications of the theory of groups of linear substitutions and of group-characteristics
On the invariants of groups of linear substitutions
On the graphical representation of a group
On the graphical representation of groups
On congruence groups
Notes
Index of technical terms
Index of authors quoted
General index
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Theory of Groups of Finite Order

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