On finite d‐maximal groups

Let d be a positive integer. A finite group is called d-maximal if it can be generated by precisely d elements, while its proper subgroups have smaller generating sets. For d is an element of{1,2}, the d-maximal groups have been classified up to isomorphism and only partial results have been proven for larger d. In this work, we prove that a d-maximal group is supersolvable and we give a characterization of d-maximality in terms of so-called maximal (p,q)-pairs. Moreover, we classify the maximal (p,q)-pairs of small rank obtaining, as a consequence, a full classification of the isomorphism classes of 3-maximal finite groups.