该文分类了任意两个非交换元均生成 p3阶子群的有限 p -群. 作为推论, 完全解决了文献[1]中提出的第237个问题: 对于所有的 x, y ∈ G, 研究满足条件( x, y) | ≤ p3的 p -群 G.
In this note we classify finite p-groups in which any two noncommutative elements generate a subgroup of order p^3. As a consequence, we solve the research problem No. 237 in [1]: Study the p-groups G such that ( x, y) | ≤ p3 for all x, y ∈ G.