Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584414 | Journal of Algebra | 2015 | 15 Pages |
Abstract
A subset S of a group G invariably generates G if G=〈sg(s)|s∈S〉G=〈sg(s)|s∈S〉 for each choice of g(s)∈Gg(s)∈G, s∈Ss∈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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
William M. Kantor, Alexander Lubotzky, Aner Shalev,