Author

Pablo Spiga

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Preprint Oct 2026

On the maximum relational complexity of affine groups

Let $G$ be a group of permutations of a set $\Omega$. The relational complexity $\mathrm{RC}(G)$ is the least integer $r\geq 2$ such that the $G$-orbit of every finite tuple is determined by the $G$-orbits of its $r$-subtuples; there is currently only a small collection of groups $G$ for which $\mathrm{RC}(G)$ is known...

Coen del Valle, Nick Gill, Pablo Spiga · 0 citations

Preprint Sep 2026

Sharp bounds for intervals in finite subgroup lattices

Let H be a subgroup of a finite group G, and put n = [G:H]>1. If p is the least prime divisor of n, we prove that the number of subgroups K with H<= K<= G is less than c(p) n^((log_p n)/4). Here c(p) is the product of (1 - p^(-j))^(-1) over all positive integers j, multiplied by the sum of p^(-z^2) over all integers z....

S. Palcoux, Pablo Spiga · 1 citation