On Finite D-maximal Groups

Lucchini, Andrea and Sabatini, Luca and Stanojkovski, Mima (2023) On Finite D-maximal Groups. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. pp. 1-17. ISSN 0024-6093 (print); 1469-2120 (online)

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Abstract

Let d be a positive integer. A finite group is called d-maximal if it can be generated by precisely d-elements, whereas its proper subgroups have smaller generating sets. For d ∈ {1, 2}, the d-maximal groups have been classified up to isomorphism and only partial results have been proved for larger d. In this work, we prove that a d-maximal group is supersolvable and we give a characterisation of d-maximality in terms of so-called maximal (

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