Invariable generation and the chebotarev invariant of a finite group

By William M. Kantor, Alexander Lubotzky, A. Shalev. 2010

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A subset S of a finite group G invariably generates G if G = for each choice of g(s) 2 G; s 2 S. We give a tight upper bound on the minimal size of an invariable generating set for an arbitrary finite group G. In response to a question in [KZ] we also bound the size of a randomly chosen set of elements of G that is likely to generate G invariably. Along the way we prove that every finite simple group is invariably generated by two elements.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/6a4eb048d67607d88472f15ce69295f44cf1ac4b