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A subset S of a group G invariably generates G if G = <s^(g(s)) | s in S> foreach choice of g(s) in G, s in S. In this paper we study invariable generationof infinite groups, with emphasis on linear groups. Our main result shows thata finitely generated linear group is invariably generated by some finite set ofelements if and only if it is virtually solvable. We also show that theprofinite completion of an arithmetic group having the congruence subgroupproperty is invariably generated by a finite set of elements.

Invariable Generation of Infinite Groups