{"product_id":"burnside-problem-and-identities-in-groups-book-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","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52627290718481,"sku":null,"price":0.0,"currency_code":"USD","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52627291439377,"sku":"NLS9783642669347","price":68.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642669347.jpg?v=1761693163","url":"https:\/\/www.worldofbooks.com\/products\/burnside-problem-and-identities-in-groups-book-sergej-i-adian-9783642669347","provider":"World of Books ","version":"1.0","type":"link"}