Some Properties And Classification Problem About Basic P-Groups

Assume G is a finite p-group and H is a subgroup of G. If H′<G′whenever H <G, then G is called a basic p-group. In this paper, someproperties about basic p-groups are obtained. In particular, A sufcientand necessary condition for a finite p-group to be a basic p-group are given.Moreover, Finite p-groups satisfying Φ(G′)G3=1and all of non-abeliansubgroups are basic are classified. Finally, By using Magma some informa-tion about basic p-groups of small order are also given.