2011/08/02 by Cristina Acciarri, Acciarri, Cristina, Gustavo A. Fernández‐Alcober +2
Computer Science · Mathematics · #20D15 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20D15 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1108.0547
8 pages, to appear in Proceedings of the Ischia Group Theory Conference 2010
arxiv created 2011/08/02 · openalex publication_date 2011/08/02 · arxiv updated 2011/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If G is a finitely generated powerful pro-p group satisfying a certain law v=1, and if G can be generated by a normal subset T of finite width which satisfies a positive law, we prove that G is nilpotent. Furthermore, the nilpotency class of G can be bounded in terms of the prime p, the number of generators of G, the law v=1, the width of T, and the degree of the positive law. The main interest of this result is the application to verbal subgroups: if G is a p-adic analytic pro-p group in which all values of a word w satisfy positive law, and if the verbal subgroup w(G) is powerful, then w(G) is nilpotent.