On finite d$d$‐maximal groups

Abstract

AbstractLet be a positive integer. A finite group is called ‐maximal if it can be generated by precisely elements, whereas its proper subgroups have smaller generating sets. For , the ‐maximal groups have been classified up to isomorphism and only partial results have been proved for larger . In this work, we prove that a ‐maximal group is supersolvable and we give a characterisation of ‐maximality in terms of so‐called maximal ‐pairs. Moreover, we classify the maximal ‐pairs of small rank obtaining, as a consequence, the classification of the isomorphism classes of 3‐maximal finite groups.