الفهرس 
IntroductionOnly 14 pages are availabe for public view
 |  | from | 108 |  |  |
| | | from | 108 | | |
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.