A Course on Finite Groups introduces the fundamentals of group theory to advanced undergraduate and beginning graduate students. Based on a series of lecture courses developed by the author over many years, the book starts with the basic definitions and examples and develops the theory to the point where a number of classic theorems can be proved. The topics covered include: homomorphisms; isomorphisms and actions; Sylow theory, products and Abelian groups; series, and nilpotent and soluble groups; and an introduction to the classificationof the finite simple groups. A number of groups are described in detail and the reader is encouraged to work with one of the many computer algebra packagesavailable to construct and experience 'actual' groups for themselves in orderto develop a deeper understanding of the theory and the significance of the theorems. Numerous exercises, of varying levels of difficulty, help to test understanding. " Combines physical book form with material on the internet so that students can use the physical book as a textbook and lecturers can use the website as a source of exercises, as well as providing more advanced students with a higher degree of material INDICE: The Group Concept.- Elementary Group Properties.- Group Construction and Representation.- Homomorphisms.- Action and the Orbit-Stabiliser Theorem.- p-Groups and Sylow Theory.- Products and Abelian Groups.- Groups of Order 24, Three Examples.- Series, Jordan Hölder Theorem and the Extension Problem.-Nilpotency.- Solubility.- Simple Groups of Order Less Than 10000.- Representation and Character Theory.- Character Tables and Theorems of Burnside and Frobenius.- Appendices.
- ISBN: 978-1-84882-888-9
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 290
- Fecha Publicación: 01/12/2009
- Nº Volúmenes: 1
- Idioma: Inglés
- Inicio /
- MATEMÁTICAS /
- ÁLGEBRA