{"product_id":"the-burnside-problem-and-identities-sergej-i-adian-9783642669347","title":"The Burnside Problem and Identities in Groups","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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Sergej I. Adian\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3642669344\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783642669347\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/16\/2011\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 314\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.17lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.61h x 6.69w x 0.69d","brand":"Sergej I. Adian","offers":[{"title":"Paperback","offer_id":44761337823487,"sku":"9783642669347","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_d6af7f0e-1f21-4d73-b42c-590030971084.jpg?v=1706681044","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-burnside-problem-and-identities-sergej-i-adian-9783642669347","provider":"WR Book House","version":"1.0","type":"link"}