On the intersection of maximal supersoluble subgroups of a finite group

Abstract

The hyper-generalized-center genz∗(G) of a finite group G coincides with the largest term of the chain of subgroups 1 = Q₀(G) ≤ Q1(G) ≤ . . . ≤ Qᵼ(G) ≤ . . . where Qᵢ(G)/Qᵢ₋₁(G) is the subgroup of G/Qᵢ₋₁(G) generated by the set of all cyclic S -quasinormal subgroups of G/Qᵢ₋₁(G). It is proved that for any finite group A, there is a finite group G such that A ≤ G and genz∗(G) ≠ Int𝔘(G).