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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Author  :  S.I. Adian 
Publisher  :  SpringerVerlag 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 
Rating  : 
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