Central extensions of some linear cycle sets

TL;DR

This paper computes all central extensions of certain linear cycle sets with cyclic abelian groups of prime power order, expanding understanding of their algebraic structure.

Contribution

It provides a complete classification of central extensions for a family of linear cycle sets with cyclic prime power order groups.

Findings

Explicit descriptions of all central extensions for the given linear cycle sets.

A comprehensive classification within the specified family.

Enhanced understanding of the algebraic structure of these cycle sets.

Abstract

For each member $\mathcal{A}$ of a family of linear cycle sets whose underlying abelian group is cyclic of order a power of a prime number, we compute all the central extensions of $\mathcal{A}$ by an arbitrary abelian group.