The Formal Context of Saturated Transfer Systems on Finite Abelian Groups

TL;DR

This paper characterizes the formal context of saturated transfer systems on finite abelian groups and computes the total number of such systems for a specific group, revealing the complexity of their structure.

Contribution

It provides a detailed description of the formal context for saturated transfer systems and calculates their total count on a particular finite abelian group, advancing understanding in this area.

Findings

Describes the reduced formal context of saturated transfer systems on finite abelian groups.

Computes over 13 trillion saturated transfer systems for the group C_5^3.

Highlights the combinatorial complexity of transfer systems on finite abelian groups.

Abstract

We describe the reduced formal context of the lattice of saturated transfer systems on a finite abelian group. As an application, we compute that there are 13,784,538,270,571 saturated transfer systems on the elementary abelian group $C_5^3$.