The Burnside Problem and Identities in Groups
Author | : Sergej I. Adian |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2011-12-16 |
ISBN-10 | : 3642669344 |
ISBN-13 | : 9783642669347 |
Rating | : 4/5 (44 Downloads) |
Download or read book The Burnside Problem and Identities in Groups written by Sergej I. Adian and published by Springer. This book was released on 2011-12-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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