Some Results About A_t-groups

We call a p-group G an A_t-group if G has a nonabelian subgroup ofindex pt1but all its subgroups of index ptare abelian.This paper consists of four chapters. Chapter I is an introduction tothis paper. Chapter II gives a list of prelininaries for this paper. In ChapterIII, we classify A2-groups and A3-groups in which a cyclic subgroup iscontained in a A1-subgroup, respectively. Moreover, we also classify A3-groups in which a cyclic(abelian) subgroup is contained in a A1-subgroupand a A1-subgroup is contained in a A2-subgroup, respectively. In ChapterIV, we prove some properties of A_t-groups(t≥3).