2025/01/14 by Jorge A. Guccione, Guccione, Jorge, Juan J. Guccione +3 · 1 citation
Computer Science · Engineering · Mathematics · #16T25 #20E22 #55N35 #Advanced Graph Theory Research #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2501.08357
openalex publication_date 2025/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper explores the cohomology of linear cycle sets, focusing on extensions of a specific linear cycle set H by an abelian group I. We derive explicit formulas for the second cohomology group, which classifies these extensions, and establish conditions under which the extensions are fully determined. Key results include a characterization of extensions when I lies in the socle of the extended structure and H is trivial, and the construction of explicit examples for both trivial and non-trivial cases. The paper provides a systematic approach to understanding the structure of these extensions, with applications to various families of abelian groups.