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OverviewThis is an elementary introduction to the congruence subgroup problem, a problem which deals with number theoretic properties of groups defined arithmetically. The novelty and, indeed, the goal of this book is to present some applications to group theory as well as to number theory which have emerged in the last fifteen years. No knowledge of algebraic groups is assumed and the choice of the examples discussed seeks to convey that even these special cases give interesting applications. After the background material in group theory and number theory, solvable groups are treated first and some generalisations are presented using class field theory.Then the group SL(n) over rings of S-integers is studied. The methods involved are very different from the ones employed for solvable groups. Group theoretic properties like presentations and central extensions are extensively used. Several proofs which appeared after the original ones are discussed. The last chapter has a survey of the status of the congruence subgroup problem for general algebraic groups. Only outlines of proofs are given here and with a sufficient understanding of algebraic groups the proofs can be completed. The book is intended for beginning graduate students. Many exercises are given. Full Product DetailsAuthor: B. SuryPublisher: Hindustan Book Agency Imprint: Hindustan Book Agency Volume: No. 24 ISBN: 9788185931388ISBN 10: 8185931380 Pages: 318 Publication Date: 01 January 2003 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Out of Print Availability: Awaiting stock Table of ContentsContents: A review of some basic notions; Congruence subgroups in solvable groups; SL2--The negative solutions; SLn(OS) - The positive cases of CSP; Applications of the CSP; CSP in general algebraic groups; Appendix: Moor's local uniqueness theoremReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |