Group representation theory. Part A: Ordinary Representation Theory
Larry L Dornhoff, "Group representation theory. Part A: Ordinary Representation Theory"
English | 1971 | ISBN: 0824711475 | DJVU | pages: 264 | 6,6 mb
English | 1971 | ISBN: 0824711475 | DJVU | pages: 264 | 6,6 mb
This book grew out of a year course in representation theory of finite groups given at the University of Illinois during 1969-1970. Its primary purpose is to provide a readable account of several major applications of representation theory to the structure of finite groups. The book should serve well as a text for a graduate course in representation theory and be useful for individual study by graduate students and mathematicians wishing to familiarize themselves with the subject. Part A separately should be useful as a text for a course in ordinary representation theory, with applications; exercises have been included in Part A to aid in this purpose. This book presupposes knowledge of only several basic topics in algebra. These include the Sylow theorems and the structure of finite abelian groups from group theory; the structure of finitely generated modules over principal ideal domains; the notion of tensor product of modules over noncommutative rings; and occasionally basic Galois theory of fields. In Part A, we begin by developing the structure theory for semi-simple rings with unit.
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