الفهرس | Only 14 pages are availabe for public view |
Abstract Let n >1 be an integer. A group G is called n-rewritable if for every n-tuple (x1,x2,…,xn) of the elements of G there exist distinct permutations τ ، σ E Symn, such that xσ(1) xσ(2)… xσ(n)= xτ(1) xτ(2)…. xτ(n). We also use Qn to denote the class of groups having this property. If one can always choose τ = 1, one obtains the class of Pn-groups (npermutable groups) The complete classification of these classes were given in [6] and [19] respectively. It is shown there that the class of such groups coincides with the class of finite-by-abelian- by-finite groups. Our goal is to continue the study of structure of these classes and its various generalizations. In fact, we have obtained significant new results on these groups depending on bounding the orders of certain subgroups and bounding the exponents of certain homomorphic images. Moreover, we proved the long standing conjecture of Blyth that nrewritable groups are m-permutable for a suitable explicit function m of n. These results improve the past results in the literature. |