A characterization of powerful p-groups |
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| Authors: | Jon González-Sánchez Amaia Zugadi-Reizabal |
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| Affiliation: | 1. Departamento de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco — Euskal Herriko Unibertsitatea UPV/EHU, Barrio Sarriena, S/N, 48940, Leioa, Spain
2. Departamento de Didáctica de las Matemáticas y de las Ciencias Experimentales Escuela Universitaria de Magisterio de Bilbao, Universidad del País Vasco — Euskal Herriko Unibertsitatea UPV/EHU, Barrio Sarriena, S/N, 48940, Leioa, Spain
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| Abstract: | In [10] Benjamin Klopsch and Ilir Snopce recently posted the conjecture that for p ≥ 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 (|Ω1(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 ≥ 5. |
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