[GAP Forum] Normal closure of a nilpotent subgroup

[Jim Heckman]

On 26-Apr-2007, Dan Lanke <dan_lanke at yahoo.com>
wrote in message <945425.15512.qm at web63312.mail.re1.yahoo.com>:

> Dear GAP Forum,
>
> I am trying to find an example of a finite group G with a subnormal
> nilpotent subgroup H such that the normal closure of H in G is not
> nilpotent. I am not
> sure if such an example exists.  I used GAP to see that no such example
> exists for |G| < 190. I run into memory problems with the computer for
> larger groups. Any suggestions please?
>
> Thanks,
> DL

Surely you've left out some condition.  As written, wouldn't
G = S_3, H = A_3 qualify?

Perhaps you also require H to be non-normal?

-- 
Jim Heckman