Invariable generation and the chebotarev invariant of a finite group

Details Invariable generation and the chebotarev invariant of a finite group Invariable generation and the chebotarev invariant of a finite group

2010-10-27

arxiv.org/abs/1010.5722v2

Mathematics

Group Theory

Improved version

Scientific paper

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.

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