On Thu, September 19, 2013 8:05 pm, yassine Guerboussa wrote:
> I will be pleased if one can help in writing a program such that,
> For a group $G$ (usually, a small group in GAP library), it computes the
> subgroup
> generatedby the elements that are not left n-Engel, for some fixed n.
> Recall that an element $a$ in $G$ is left n-Engel if it satisfies the
> identity$[x,a,...,a]=1$, where $a$ occurs $n$ times (the commutator is left
> normed).
I think the following should serve the purpose, as long as your groups are
small:
SubgroupGeneratedByElementsWhichAreNotLeftnEngel := function ( G, n )
local elms, gens, H;
elms := AsList(G);
gens := Filtered(elms,
a->ForAny(elms,x->not IsOne(LeftNormedComm(
Concatenation([x],ListWithIdenticalEntries(n,a))))));
H := Group(gens,One(G));
return H;
end;
Hope this helps,
Stefan Kohl
-----------------------------------------------------------------------------
http://www.gap-system.org/DevelopersPages/StefanKohl/
-----------------------------------------------------------------------------
_______________________________________________
Forum mailing list
Forum@mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum
