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The expected number of random elements to generate a finite group

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Abstract

We will see that the expected number of elements of a finite group G which have to be drawn at random, with replacement, before a set of generators is found, can be determined using the Möbius function defined on the subgroup lattice of G. We will discuss several applications of this result.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121, Padua, Italy

    Andrea Lucchini

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  1. Andrea Lucchini
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Correspondence to Andrea Lucchini.

Additional information

Communicated by J. S. Wilson.

A. Lucchini was partially supported by Università di Padova (Progetto di Ricerca di Ateneo: “Invariable generation of groups”).

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Lucchini, A. The expected number of random elements to generate a finite group. Monatsh Math 181, 123–142 (2016). https://doi.org/10.1007/s00605-015-0789-5

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  • DOI: https://doi.org/10.1007/s00605-015-0789-5

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