A characterization of powerful p-groups

作者：Gonzalez Sanchez Jon^*; Zugadi Reizabal Amaia

来源：Israel Journal of Mathematics, 2014, 202(1): 321-329.

DOI：10.1007/s11856-014-1072-5

In [10] Benjamin Klopsch and Ilir Snopce recently posted the conjecture that for p %26gt;= 3 and G a torsion-free pro-p group, d(G) = dim(G) is a sufficient and necessary condition for the pro-p group G to be uniform. They pointed out that this follows from the more general question of whether for a finite p-group d(G) = log (p) (|Omega(1)(G)|) is a sufficient and necessary condition for the group G to be powerful. In this short note we will give a positive answer to this question for p %26gt;= 5.

• 出版日期2014-7