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Invariable Generation of Infinite Groups

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arxiv 1407.4631 v1 pith:KKH3GFVT submitted 2014-07-17 math.GR

William M. Kantor , Alexander Lubotzky , Aner Shalev This is my paper · ORCID
classification math.GR
keywords generatedgroupgroupsinvariablyelementsfinitegenerationinfinite
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A subset S of a group G invariably generates G if G = <s^(g(s)) | s in S> 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.

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  1. Alternating Groups and Embeddings into Groups Invariably Generated by Two Prime-Order Elements

    math.GR 2026-08 accept novelty 7.0 of 10

    For distinct primes p and q, the alternating group A_n, for every sufficiently large n, does not embed into any finite group invariably generated by an order-p and an order-q element.

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