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Recognizing a finite group from the generating properties of its subsets

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Abstract

We assume to have information about the generating properties of the subsets of a finite group G. In particular, we consider the two following situations. We know, for every subset X of G, whether X is a generating set of G. We know the graph whose vertices are the subsets of G and in which there is an edge connecting X and Y if and only if \(X\cup Y\) is a generating set of G. We discuss how this kind of information can be used to discover properties of the group G.

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  1. Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy

    Andrea Lucchini

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  1. Andrea Lucchini
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Correspondence to Andrea Lucchini.

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Lucchini, A. Recognizing a finite group from the generating properties of its subsets. Annali di Matematica 200, 117–123 (2021). https://doi.org/10.1007/s10231-020-00986-3

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  • DOI: https://doi.org/10.1007/s10231-020-00986-3

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