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)