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Geometry of Defining Relations in Groups A.Yu. Olshanskii

Geometry of Defining Relations in Groups

A.Yu. Olshanskii

Published October 31st 1991
ISBN : 9780792313946
Hardcover
505 pages
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 About the Book 

The main feature of this book is a systematic application of elementary geometric and topological techniques for solving problems that arise naturally in algebra. After an account of preliminary material, there is a discussion of a geometrically intuitive interpretation of the derivation of consequences of defining relations of groups. A study is made of planar and certain other two-dimensional maps connected with well-known problems in general group theory, such as the problems of Burnside and O. Yu. Schmidt. The method of cancellation diagrams developed here is applied to these and to a series of other problems. This monograph is addressed to research workers and students in universities, and may be used as a basis for a series of specialized lectures or seminars.