Theory of Groups of Finite Order Cambridge Library Collection - Mathematics Series

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.