The Burnside Problem and Identities in Groups (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge)

Sergej I. Adian

ISBN 10: 3642669344 / ISBN 13: 9783642669347

Published by Springer Berlin Heidelberg, 2012

About this Item

reprint edition. 332 pages. 9.50x6.70x0.90 inches. In Stock.

Seller Inventory # x-3642669344

Bibliographic Details

• Title: The Burnside Problem and Identities in Groups (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge)
• Publisher: Springer Berlin Heidelberg
• Publication Date: 2012
• Language: English
• ISBN 10: 3642669344
• ISBN 13: 9783642669347
• Binding: Paperback
• Condition: Brand New
• Weight: 0.55 kilograms

About this title

Synopsis

Three years have passed since the publication of the Russian edition of this book, during which time the method described has found new applications. In [26], the author has introduced the concept of the periodic product of two groups. For any two groups G and G without elements of order 2 and for any 1 2 odd n ~ 665, a group G @ Gmay be constructed which possesses several in­ 1 2 teresting properties. In G @ G there are subgroups 6 and 6 isomorphic to 1 2 1 2 G and G respectively, such that 6 and 6 generate G @ G and intersect 1 2 1 2 1 2 in the identity. This operation "@" is commutative, associative and satisfies Mal'cev's postulate (see [27], p. 474), i.e., it has a certain hereditary property for subgroups. For any element x which is not conjugate to an element of either 6 1 or 6 , the relation xn = 1 holds in G @ G • From this it follows that when 2 1 2 G and G are periodic groups of exponent n, so is G @ G • In addition, if G 1 2 1 2 1 and G are free periodic groups of exponent n the group G @ G is also free 2 1 2 periodic with rank equal to the sum of the ranks of G and G • I believe that groups 1 2

Language Notes

Text: English, Russian (translation)