On the number of generators needed for free profinite products of finite groups

2007/03/05 by Miklós Abért, Miklos Abert, Abert, Miklos +3
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0703105

14 pages

arxiv created 2007/03/05 · openalex publication_date 2007/03/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide lower estimates on the minimal number of generators of the profinite completion of free products of finite groups. In particular, we show that if C₁,...,C_n are finite cyclic groups then there exists a finite group G which is generated by isomorphic copies of C₁,...,C_n and the minimal number of generators of G is n.

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