Read e-book online An Introduction to the Theory of Groups (Graduate Texts in PDF

By Joseph J. Rotman

ISBN-10: 0387942858

ISBN-13: 9780387942858

An individual who has studied summary algebra and linear algebra as an undergraduate can comprehend this e-book. the 1st six chapters supply fabric for a primary direction, whereas the remainder of the e-book covers extra complex subject matters. This revised variation keeps the readability of presentation that used to be the hallmark of the former variations. From the experiences: "Rotman has given us a truly readable and invaluable textual content, and has proven us many appealing vistas alongside his selected route." --MATHEMATICAL REVIEWS

Retail PDF from Springer; a number of chapters mixed into one dossier; scanned, searchable.

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Extra resources for An Introduction to the Theory of Groups (Graduate Texts in Mathematics, Volume 148)

Sample text

Assume that T

It is clear that cp-1(X) contains the right side. For the reverse inclusion, let (s, t), (a, f) E cp-1(X); that is, s, a E S, t, f E T, and st = x = af. Thus, s-la = tf- 1 E S n T; let d = s-la = tf- 1 denote their common value. Then a = S(S-l a) = sd and d- 1t = felt = f, as desired. • n There is one kind of subgroup that is especially interesting because it is intimately related to homomorphisms. Definition. A subgroup K :::;; G is a normal subgroup, denoted by K gKg- 1 = K for every g E G.

If Gis a finite group and a E Proof. By definition, the order of a is from Lagrange's theorem. • G. Then the order of a divides IGI· l

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An Introduction to the Theory of Groups (Graduate Texts in Mathematics, Volume 148) by Joseph J. Rotman

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