Limiting density of global transfer-system contexts for all finite groups

Determine the limiting density of the formal-context matrices associated with the families of finite groups of order at most n, and establish whether it satisfies 0.5 < lim_n δ(𝒢_n) < 1.

Background

For each family 𝒢_n of finite groups of order at most n, the paper associates a binary formal-context matrix C(𝒢_n) whose entries encode containment relations between global transfer systems generated and antigenerated by endopure transfers. The density δ(𝒢_n) is the proportion of entries equal to one.

Computations show that the density does not appear to approach 1, unlike the corresponding density for bounded-order finite abelian groups. The authors therefore formulate a conjectural lower and upper bound for the limiting density over all finite groups.