2023/02/24 by André Nies, Nies, Andre, Frank Stephan +1
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Logic (math.LO) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2302.12446
openalex publication_date 2023/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider word automaticity for groups that are nilpotent of class 2 and have exponent a prime p. We show that the infinitely generated free group in this variety is not word automatic. In contrast, the infinite extra-special p-group Ep is word automatic, as well as an intermediate group Hp which has an infinite centre. In the last section we introduce a method to show automaticity of central extensions of abelian groups via co-cycles.