Groups that are not generated by certain $$\mathfrak{X}$$ -abnormal subgroups

Abstract

In the theory of formations the concept of an\(\mathfrak{X}\)-normal maximal subgroup is widely used, being some formation [1]. In this note the concept of\(\mathfrak{X}\) normality is introduced for arbitrary subgroups. Subgroups that are not\(\mathfrak{X}\)-normal are called\(\mathfrak{X}\)-abnormal. Finite groups that are not generated by S-abnormal n-th maximal subgroups (n=1, 2, 3, 4) are studied, where S is the formation of all supersolvable groups. The general nature of the results of [3–6] is brought out.