Richard Schroeppel <rcs@CS.Arizona.EDU> wrote: ...
More generally, when is G(MN)=G(M)*G(N)? If gcd(M,N)=1, we expect at least >= just from the cross products, after we've proved they are all distinct. Groupies?
If I'm reasoning correctly, then if (M,N)=1 G(MN)=G(M)G(N) iff MN is a nilpotent number. I think a finite group is nilpotent iff it's the product of its Sylow subgroups (subgroups of order p^k where p^k|n, but p^(k+1) not|n) Note: that's not the definition of nilpotent group, but a consequence of the definition. Nilpotent numbers are in A056867 They should include all abelian numbers A051532 and all prime powers A000961. Unfortunately the only nontrivial nilpotent number to make the list is 135. We should have a sequence of nilpotent numbers that are not abelian and not prime powers I can't read dvi files easily. Maybe you can look at the paper cited and get something from it. As far as G(MN)=G(M)G(N) when (M,N) != 1 I can't say, but I'd be surprised if it were ever true.