BTW, he isn't assuming the ring has a unit, and IIRC he says that much less is known about that case. In case someone is going to program this. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Tue, Jan 5, 2021 at 8:49 PM Marc LeBrun <mlb@well.com> wrote:
there are infinitely many n such that there are more groups with n elements than rings with n elements
Hm, I'm woefully uneducated in this stuff, but for this to even be an interesting question I think this says there must be groups that can be extended to rings in more than one way (since every ring an additive group augmented with a multiplicative operator).
That suggests a table for the OEIS: T[n,k] = number of groups of order n that can be extended to (at most) k different rings.
T[n,0] would be the number of groups of order n that cannot be augmented to be rings.
Row sum over k of T[n,k] = number of groups of order n.
Row sum over k of k * T[n,k] = number of rings of order n
I'm curious: what is the smallest group G that supports more than one ring? (ie a G with min n such that T[n, some k > 1] is > 0)
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