2014/07/17 by William M. Kantor, Alexander Lubotzky, Kantor, William M. +3 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1407.4631
openalex publication_date 2014/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A subset S of a group G invariably generates G if G = for each choice of g(s) in G, s in S. In this paper we study invariable generation of infinite groups, with emphasis on linear groups. Our main result shows that a finitely generated linear group is invariably generated by some finite set of elements if and only if it is virtually solvable. We also show that the profinite completion of an arithmetic group having the congruence subgroup property is invariably generated by a finite set of elements.