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Dears,

Hello

I need a collector function which works as follows,

as far as I know a such function does not exist in

GAP (say me

if I am wrong) so my question is essentially is:

Have a such function been written and now it is

available!!??

If one exists then it will work as follows:

Let $x_1,\dots, x_n$ be the generators of the free

group of rank $n$ and $k$ be a positive integer.

the input of the function is : $x_1,\dots, x_n$ and

$k$.

the output is the list $w_1,\dots, w_s$ satisfying the

following conditions:

$(x_1 \cdots x_n)^k=x_1^k \cdots x_n^k w_1 \cdots w_s$ for all $i=1,\dots, s$ $w_i=[x_{j_1},\dots,x_{j_{t_i}}]$ for some $j_1, \dots, j_{t_i}$ in $\{ 1, \dots, n \}$ and $t_1 \leq t_2 \leq \dots \leq t_s$. ( "$[y_1,\dots, y_m]$" donotes the usual left normed commutator defined inductively by $[x,_0 y]=x$, $[x,_1 y]:=[x,y]:=x^{-1}y^{-1}xy$ and $[y_1,\dots,y_m]=[[y_1,\dots,y_{m-1}],y_m]$ for all $m>1$.

Of course the commutators $w_i$'s are depend to the

way of collecting $x_i$'s and in practice they are

not necessarily unique.

Thanks for any help.

With best wishes

Alireza Abdollahi

=====

Alireza Abdollahi

Department of Mathematics

University of Isfahan,

Isfahan 81744,Iran

e-mail: alireza_abdollahi@yahoo.com

URL: http://www.abdollahi.8m.net

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