LMS: 188 Local Analysis Order Thm

LMS: 188 Local Analysis Order Thm book cover

LMS: 188 Local Analysis Order Thm

Author(s): Helmut Bender (Author)

  • Publisher: Cambridge University Press
  • Publication Date: 21 Aug. 2008
  • Edition: Revised ed.
  • Language: English
  • Print length: 188 pages
  • ISBN-10: 0521457165
  • ISBN-13: 9780521457163

Book Description

In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable. This proof, which ran for 255 pages, was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a revision and expansion of the first half of the proof of the Feit–Thompson theorem. Simpler, more detailed proofs are provided for some intermediate theorems. Recent results are used to shorten other proofs. The book will make the first half of this remarkable proof accessible to readers familiar with just the rudiments of group theory.

Editorial Reviews

Review

‘This book is written well … the authors have succeeded both in simplifying the proof of the Odd Order Theorem and in making it accessible to a wider audience.’ Paul Flavell, Bulletin of the London Mathematical Society

Book Description

The book presents a new version of the local analysis section of the Feit–Thompson theorem.

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LMS: 46 P Adic Analysis: A Short Course on Recent Work

LMS: 46 P Adic Analysis: A Short Course on Recent Work book cover

LMS: 46 P Adic Analysis: A Short Course on Recent Work

Author(s): Koblitz (Author)

  • Publisher: Cambridge University Press
  • Publication Date: 12 Jan. 2008
  • Edition: 1st
  • Language: English
  • Print length: 168 pages
  • ISBN-10: 1845889118
  • ISBN-13: 9780521280600

Book Description

This introduction to recent work in p-adic analysis and number theory will make accessible to a relatively general audience the efforts of a number of mathematicians over the last five years. After reviewing the basics (the construction of p-adic numbers and the p-adic analog of the complex number field, power series and Newton polygons), the author develops the properties of p-adic Dirichlet L-series using p-adic measures and integration. p-adic gamma functions are introduced, and their relationship to L-series is explored. Analogies with the corresponding complex analytic case are stressed. Then a formula for Gauss sums in terms of the p-adic gamma function is proved using the cohomology of Fermat and Artin-Schreier curves. Graduate students and research workers in number theory, algebraic geometry and parts of algebra and analysis will welcome this account of current research.

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