The Number Of Minimal Non-abelian Subgroups In A₁¹-groups

Suppose that G is a finite p-group. If all subgroups of index pt of G are abelian and at least one subgroup of index pt-1of G is not abelian, then G is called an At-group. The p-groups containing an A1-subgroup of index p is called an A11-group. In this paper, we give the number of minimal non-abelian subgroups in A11-groups containing at least two A1-subgroups of index p.