Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Profinite Groups and Residual Finiteness
 
Gareth Wilkes Jesus College, University of Cambridge, UK
A publication of European Mathematical Society
Hardcover ISBN:  978-3-98547-078-5
Product Code:  EMSTEXT/29
List Price: $65.00
AMS Member Price: $52.00
Please note AMS points can not be used for this product
Click above image for expanded view
Profinite Groups and Residual Finiteness
Gareth Wilkes Jesus College, University of Cambridge, UK
A publication of European Mathematical Society
Hardcover ISBN:  978-3-98547-078-5
Product Code:  EMSTEXT/29
List Price: $65.00
AMS Member Price: $52.00
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Textbooks in Mathematics
    Volume: 292024; 434 pp
    MSC: Primary 20; Secondary 06; 11; 18

    This book describes the theory of profinite groups, from the basics of the theory to topics which are active areas of current research. It is the first textbook on profinite groups to make their use in studying residually finite groups via their profinite completions a central focus.

    The first part of the book gives the subject a firm theoretical underpinning from category theory and introduces profinite groups as objects worthy of study in their own right. The reader is not expected to have a background in category theory. The connection of a residually finite group to its profinite completion is explored in detail, with emphasis on various separability properties and profinite rigidity.

    The study of group cohomology is a key tool in the exploration of profinite groups. The central portion of this book gives a standalone first course in group cohomology before showing the modification of this theory for use with profinite groups. There is special emphasis on the unique features of profinite group cohomology, such as Pontryagin duality and Sylow theory.

    Later chapters of the book collect together for the first time important results concerning the relation of the cohomology of a group to that of its profinite completion and introduce the concept of an action of a profinite group on a profinite tree. This material aims to be a useful reference for researchers, as well as a learning resource.

    A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

    Readership

    Graduate students and researchers interested in group theory, in particular, profinite groups.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 292024; 434 pp
MSC: Primary 20; Secondary 06; 11; 18

This book describes the theory of profinite groups, from the basics of the theory to topics which are active areas of current research. It is the first textbook on profinite groups to make their use in studying residually finite groups via their profinite completions a central focus.

The first part of the book gives the subject a firm theoretical underpinning from category theory and introduces profinite groups as objects worthy of study in their own right. The reader is not expected to have a background in category theory. The connection of a residually finite group to its profinite completion is explored in detail, with emphasis on various separability properties and profinite rigidity.

The study of group cohomology is a key tool in the exploration of profinite groups. The central portion of this book gives a standalone first course in group cohomology before showing the modification of this theory for use with profinite groups. There is special emphasis on the unique features of profinite group cohomology, such as Pontryagin duality and Sylow theory.

Later chapters of the book collect together for the first time important results concerning the relation of the cohomology of a group to that of its profinite completion and introduce the concept of an action of a profinite group on a profinite tree. This material aims to be a useful reference for researchers, as well as a learning resource.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and researchers interested in group theory, in particular, profinite groups.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.