Theory of Groups of Finite Order

This foundational work, originally published in 1897 but reissued here in its expanded 1911 edition, remained the standard reference for many years.

William Burnside (Author)

9781108050326, Cambridge University Press

Paperback / softback, published 7 June 2012

544 pages, 1 colour illus.
21.6 x 14 x 3.1 cm, 0.68 kg

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
1. On permutations
2. The definition of a group
3. On the simpler properties of a group which are independent of its mode of representation
4. Further properties of a group which are independent of its mode of representation
5. On the composition-series of a group
6. On the isomorphism of a group within itself
7. On Abelian groups
8. On groups whose orders are the powers of primes
9. On Sylow's theorem
10. On permutation-groups: transitive and intransitive groups
11. On permutation-groups: transitivity and primitivity
12. On the representation of a group of finite order as a permutation-group
13. On groups of linear substitutions
14. On the representation of a group of finite order as a group of linear substitutions
15. On group-characteristics
16. Some applications of the theory of groups of linear substitutions and of group-characteristics
17. On the invariants of groups of linear substitutions
18. On the graphical representation of a group
19. On the graphical representation of groups
20. On congruence groups
Notes
Index of technical terms
Index of authors quoted
General index.

Subject Areas: Number theory [PBH]