P.hall#x2019; theorem for regularp-groups and its application to some classification problems

摘要

In 1933 P.Hall proved a basis theorem for regularp-groups. In this paper we give another proof for it; this proof allows one to construct a uniqueness basis explicitly. This method to construct uniqueness bases can be used in some classification problems for regularp-groups. Here we give an example, and as a by-product, we obtain a classification for groups of orderp4p≥5.