By David S. Dummit, Richard M. Foote

ISBN-10: 0471433349

ISBN-13: 9780471433347

"Widely acclaimed algebra textual content. This e-book is designed to provide the reader perception into the ability and sweetness that accrues from a wealthy interaction among diverse components of arithmetic. The publication conscientiously develops the idea of alternative algebraic constructions, starting from uncomplicated definitions to a couple in-depth effects, utilizing a number of examples and workouts to help the reader's knowing. during this means, readers achieve an appreciation for the way mathematical buildings and their interaction result in strong effects and insights in a couple of assorted settings."

Covers primarily all undergraduate algebra. Searchable DJVU.

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**Extra resources for Abstract Algebra (3rd Edition)**

**Sample text**

2 Lemma. Let G be a finite p-group and let N,K and W be normal subgroups of G with N

22. Let F be a torsion-free finitely generated nilpotent group, with upper central series 1 = Zo < ... < Zc = F. Then Zi/Zi-i = ZTi for certain positive integers r*i,... ,r c . Show that the upper central series of F is 1 = Zo < ... < Zc = F, and that for each i we have Zi = Z{ and Zi/Zi-i = Z^/Z^-i, where ^ denotes either profinite completion or pro-p completion. ] 23. Show that a finitely generated abelian pro-p group is isomorphic to 7jp x F for some d and some finite group F. ] 24. Let G be a finitely generated pro-p group and M, N open normal subgroups of G.

To prove (iii), put H = (N,x). e. G then [H,H] < Np < Hp (respectively, [H,H] < H4 if p = 2). For part (iv), suppose that p is odd and that [AT, W] ^ Np. Then Np < NP[N, W] = M, say. Since G is a p-group and M and N are normal in G, there exists J

### Abstract Algebra (3rd Edition) by David S. Dummit, Richard M. Foote

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