Describing groups using first-order language

2013/05/01 by Yuki Maehara, Maehara, Yuki
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR

paper · pdf · doi:10.48550/arxiv.1305.0080

arxiv created 2013/05/01 · openalex publication_date 2013/05/01 · arxiv updated 2013/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate two notions about descriptions of groups using first-order language: quasi-finite axiomatizability, concerning infinite groups, and polylogarithmic compressibility, concerning classes of finite groups.

Related

• Formal Languages and Infinite Groups
• Describing finite groups by short first-order sentences
• Languages recognised by finite semigroups, and their generalisations to objects such as trees and graphs, with an emphasis on definability in monadic second-order logic
• Conciseness of first-order formulae
• Finite axiomatizability for profinite groups