The Burnside Problem and Identities in Groups PDF ePub eBook

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The Burnside Problem and Identities in Groups free pdf 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

About S.I. Adian

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Details Book

Author : S.I. Adian
Publisher : Springer-Verlag Berlin and Heidelberg GmbH
Data Published : 16 December 2011
ISBN : 3642669344
EAN : 9783642669347
Format Book : PDF, Epub, DOCx, TXT
Number of Pages : 314 pages
Age + : 15 years
Language : English
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  • The Burnside Problem and Identities in Groups free pdfThe Burnside Problem and Identities in Groups

    Download Book Online. 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 intr