The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of finite rank, starting from first principles and using elementary methods. Part II introduces p-adic analytic groups: by taking advantage of the theory developed in Part I, it is possible to define these, and derive all the main results of p-adic Lie theory, without having to develop any sophisticated analytic machinery. Part III, consisting of new material, takes the theory further. Among those topics discussed are the theory of pro-p groups of finite coclass, the dimension subgroup series, and its associated graded Lie algebra. The final chapter sketches a theory of analytic groups over pro-p rings other than the p-adic integers.
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Book Description
The theory of p-adic analytic pro-p groups has undergone significant development since the seminal work of Lazard. This book presents a complete and self-contained account of this theory, which has applications in both group theory and number theory. This up-to-date second edition incorporates many important new results.
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Inside This Book
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We have done our best to make this book reasonably self-contained. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
topological generating set, finite coclass, restricted monomials, formal group law, topological group containing, analytic manifold structure, universal envelope, profinite group, open normal subgroup, faithful linear representation, global atlas, open subgroup, maximal proper subgroup, analytic groups, additive cosets, subgroup growth, analytic homomorphism, many isomorphism types, base for the neighbourhoods, global chart, finite rank, profinite completion, prop group, mapping log, normed ring Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lemma Let, Proposition Let, Proof Let, Theorem Let, Definition Let, Corollary Let, Lemma Suppose, Proof Suppose, Proof Write, Lemma Assume, Proof Put, Proof Parts, Proof Say, Corollary Suppose New!
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We have done our best to make this book reasonably self-contained. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
topological generating set, finite coclass, restricted monomials, formal group law, topological group containing, analytic manifold structure, universal envelope, profinite group, open normal subgroup, faithful linear representation, global atlas, open subgroup, maximal proper subgroup, analytic groups, additive cosets, subgroup growth, analytic homomorphism, many isomorphism types, base for the neighbourhoods, global chart, finite rank, profinite completion, prop group, mapping log, normed ring Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lemma Let, Proposition Let, Proof Let, Theorem Let, Definition Let, Corollary Let, Lemma Suppose, Proof Suppose, Proof Write, Lemma Assume, Proof Put, Proof Parts, Proof Say, Corollary Suppose New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 2
books:
2
books
cite this book:
- Introduction To Commutative Algebra by Michael Atiyah in Back Matter
- Commutative Algebra (Elements of Mathematics) by Nicolas Bourbaki in Back Matter
- Galois Theories (Cambridge Studies in Advanced Mathematics) by Francis Borceux in Front Matter
- Fourier Analysis and Partial Differential Equations (Cambridge Studies in Advanced Mathematics) by Rafael José Iorio Jr in Front Matter
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