If you are considering reasonably small finite groups you can use
direct methods such as

Is2Engel := function(G) return ForAll(Cartesian(G,G),
x->LeftNormedComm(x)=One(G)); end;

Robert F. Morse

On Sat, Jan 21, 2012 at 8:09 AM, Joy F. <litlejoy_m...@yahoo.com> wrote:
> Dear forum,
>
>
> How do I check if a group G is 2-Engel?
>
> Joy.
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