An introduction to abstract algebra

THIS IS A TEXTBOOK FOR STUDENTS UNDERTAKING, OR ABOUT TO UNDERTAKE, A first course in Abstract Algebra (e. g. second-year Honours students and second-or third-year Ordinary Degree students in Scottish universities; first year students in many English universities). The first edition of the book proved helpful to many such students, and it is hoped that this second edition may be found even more helpful. The main changes made in producing the se co nd edition have been the inclusion of a whole new chapter on the symmetrie group and the expansion of the existing sets of exercises, together with updating and revising of the text. The book is not an advanced treatise on group theory or on any kindred part of mathematics. But, in contrast to many elementary textbooks, it does penetrate far enough into Abstract Algebra to let the student see that the subject has worthwhile insights to offer, and to introduce hirn to some of the distinctive ways of thinking that produce interesting results. For example, in group theory, the material covered includes cyclic groups, Lagrange's theorem, homomorphisms, normal subgroups, quotient groups, and (in the new chapter) the partition of the symmetrie group of degree n into conjugacy classes and an intro duc ti on to the alternating group of degree n. Although there is only one chapter on rings (and fields), it is a lengthy chapter and covers a wide variety of ideas.