| The Burnside Problem and Identities in Groups Softcover Repri Edition Contributor(s): Adian, Sergej I. (Author), Lennox, John (Translator), Wiegold, James (Translator) |
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ISBN: 3642669344 ISBN-13: 9783642669347 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: December 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - General - Mathematics | Group Theory |
| Dewey: 512.22 |
| Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge |
| Physical Information: 0.69" H x 6.69" W x 9.61" (1.17 lbs) 314 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 |