the item on "group analogy to perfect numbers" sounds like it's just this sort of thing.
Dan wrote: > > Call a finite group G "Group perfect" if > ths sum of the orders of the proper normal subgroups of G > equals the order of G (*) . > > The cyclic group C_n has the property (*) iff n is a perfect number . > > Are there also non-abelian groups with this property ? > > Thanks
email@example.com (galathaea) wrote in message news:<firstname.lastname@example.org>...
> The modular Galois representations were shown by Ribet to have > properties in contradiction to the four properties listed above for > the representation associated to E. Thus E does not have a modular > representation.